Fixed abrasive articles and methods of forming same

ABSTRACT

A fixed abrasive article having a body including abrasive particles contained within a bond material, the abrasive particles including shaped abrasive particles or elongated abrasive particles having an aspect ratio of length:width of at least 1.1:1, each of the shaped abrasive particles or elongated abrasive particles having a predetermined position or a predetermined three-axis orientation.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application is a continuation of U.S. Non-Provisional patentapplication Ser. No. 15/087,722, filed Mar. 31, 2016, entitled “FIXEDABRASIVE ARTICLES AND METHODS OF FORMING SAME,” naming inventors CelineColet et al., which claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Patent Application No. 62/289,501, filed Feb. 1, 2016,entitled “FIXED ABRASIVE ARTICLES AND METHODS OF FORMING SAME,” naminginventors Celine Colet et al., and which claims priority under 35 U.S.C.§ 119(e) to U.S. Provisional Patent Application No. 62/259,501, filedNov. 24, 2015, entitled “FIXED ABRASIVE ARTICLES AND METHODS OF FORMINGSAME,” naming inventors Celine Colet et al., and which claims priorityunder 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No.62/141,175, filed Mar. 31, 2015, entitled “FIXED ABRASIVE ARTICLES ANDMETHODS OF FORMING SAME,” naming inventors Celine Colet et al., each ofwhich applications are incorporated by reference herein in theirentireties for all purposes.

BACKGROUND Field of the Disclosure

The following is directed to fixed abrasive articles, and moreparticularly, to fixed abrasive articles including shaped abrasiveparticles or elongated abrasive particles.

Description of the Related Art

Abrasive articles incorporating abrasive particles are useful forvarious material removal operations including grinding, finishing,polishing, and the like. Depending upon the type of abrasive material,such abrasive particles can be useful in shaping or grinding variousmaterials in the manufacturing of goods. Certain types of abrasiveparticles have been formulated to date that have particular geometries,such as triangular shaped abrasive particles and abrasive articlesincorporating such objects. See, for example, U.S. Pat. Nos. 5,201,916;5,366,523; and 5,984,988.

Previously, three basic technologies that have been employed to produceabrasive particles having a specified shape are fusion, sintering, andchemical ceramic. In the fusion process, abrasive particles can beshaped by a chill roll, the face of which may or may not be engraved, amold into which molten material is poured, or a heat sink materialimmersed in an aluminum oxide melt. See, for example, U.S. Pat. No.3,377,660. In sintering processes, abrasive particles can be formed fromrefractory powders having a particle size of up to 10 micrometers indiameter. Binders can be added to the powders along with a lubricant anda suitable solvent to form a mixture that can be shaped into plateletsor rods of various lengths and diameters. See, for example, U.S. Pat.No. 3,079,242. Chemical ceramic technology involves converting acolloidal dispersion or hydrosol (sometimes called a sol) to a gel orany other physical state that restrains the mobility of the components,drying, and firing to obtain a ceramic material. See, for example, U.S.Pat. Nos. 4,744,802 and 4,848,041.

The industry continues to demand improved abrasive materials andabrasive articles.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 includes a perspective view illustration of a fixed abrasivearticle according to an embodiment.

FIG. 2 includes a perspective view illustration of a shaped abrasiveparticle according to an embodiment.

FIG. 3A includes a perspective view illustration of a shaped abrasiveparticle in accordance with an embodiment.

FIG. 3B includes a perspective view illustration of an elongatedabrasive particle according to an embodiment.

FIG. 4A includes an illustration of a shaped abrasive particle accordingto an embodiment.

FIG. 4B includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 4C includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 4D includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 5A includes an illustration of a portion of a fixed abrasivearticle including abrasive particles in accordance with an embodiment.

FIG. 5B includes an illustration of an abrasive particle within a fixedabrasive article in accordance with an embodiment.

FIG. 5C includes an illustration of a plurality of abrasive particleswithin a fixed abrasive article according to an embodiment.

FIG. 6 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 7 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 8 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 9 includes a flowchart illustrating a method of forming a fixedabrasive article in accordance with an embodiment.

FIGS. 10A-10C include illustrations of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 11 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 12A includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 12B includes an illustration of a forming structure for forming afixed abrasive article in accordance with an embodiment.

FIG. 13 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 14 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 15 includes a flowchart illustrating a method of forming a fixedabrasive article in accordance with an embodiment.

FIG. 16 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIGS. 17A and 17B include illustrations of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 18 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 19 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 20 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 21A includes an image of elongated abrasive particles in accordancewith an embodiment.

FIGS. 21B-21C include illustrations of a forming structure in accordancewith an embodiment.

FIG. 21D includes an image of a forming structure in accordance with anembodiment.

FIGS. 22A-22B includes images of fixed abrasive articles in accordancewith an embodiment.

FIG. 22C includes a graph of orientation for the fixed abrasive articlesof FIGS. 22A-22B in accordance with an embodiment.

FIG. 23 includes a graph of cumulative Q-ratio for fixed abrasivearticles in accordance with an embodiment.

FIG. 24A includes an image of a fixed abrasive article in accordancewith an embodiment.

FIG. 24B includes an image of a forming structure in accordance with anembodiment.

FIGS. 24C-24D include images of fixed abrasive articles in accordancewith an embodiment.

FIG. 25A provides a top-down illustration of a portion of an abrasivearticle in accordance with an embodiment.

FIGS. 25B-D include illustrations of distributions in accordance with anembodiment.

FIG. 26 includes a top-down illustration of a portion of an abrasivearticle in accordance with an embodiment.

DETAILED DESCRIPTION

In accordance with an embodiment a fixed abrasive article is disclosed.The fixed abrasive article may be suitable for material removaloperations on a variety of workpieces including for example metal ormetal alloy materials. Moreover, in certain instances, the fixedabrasive articles of the embodiments herein can include bonded abrasivearticles, and more particularly, thin wheels, cut-off wheels, chop saws,roll mill grinding wheels, centerless grinding wheels, and the like.Such products may be particularly suitable for material removaloperations including for example, grinding, cutting, dicing, and thelike.

FIG. 1 includes a perspective view illustration of a fixed abrasivearticle in accordance with an embodiment. As illustrated, the fixedabrasive article 100 can have a body 101 of a generally cylindricalshape including an upper surface 102, a bottom surface 104, and a sidesurface 103 extending between the upper surface 102 and bottom surface104. It will be appreciated that the fixed abrasive article of FIG. 1 isa non-limiting example, and other shapes of the body may be utilizedincluding, but not limited to, conical, cup-shaped, depressed centerwheels (e.g., T42), and the like. Finally, as further illustrated, thebody 101 can include a central opening 185 which may be configured toaccept an arbor or shaft for mounting of the body 101 on a machineconfigured to rotate the body 101 and facilitate a material removaloperation.

The fixed abrasive article 100 can have a body 101 including abrasiveparticles, including for example, the groups of abrasive particles 105and 106, contained within the volume of the body 101. The abrasiveparticles may be contained within the three-dimensional volume of thebody 101 by a bond material 107 that can extend throughout thethree-dimensional volume of the body 101. In accordance with anembodiment, the bond material 107 can include materials such asvitreous, polycrystalline, monocrystalline, organic (e.g., resin),metal, metal alloys, and a combination thereof.

In accordance with an embodiment, the abrasive particles containedwithin the fixed abrasive 100 can include abrasive materials, includingbut not limited to oxides, carbides, nitrides, borides, oxycarbides,oxynitrides, oxyborides, superabrasives, diamond, cubic boron nitride,carbon-containing materials, and any combination thereof. In moreparticular instances, the abrasive particles may include amonocrystalline material, a polycrystalline material, a vitreousmaterial, and any combination thereof. In at least one embodiment, theabrasive particles can include a material such as alumina, zirconia,magnesia, rare-earth oxides, and a combination thereof.

Moreover, it will be appreciated that the fixed abrasive article 100 caninclude a combination of abrasive particles, including for example oneor more types of abrasive particles including for example primary andsecondary types of abrasive particles. Primary and secondary types mayrefer to the content of the abrasive particles within the body of thefixed abrasive article, wherein the primary type abrasive particles arepresent in a higher content than the secondary type of abrasiveparticles. In other instances, the distinction between primary andsecondary types of abrasive particles may be based upon the position ofthe abrasive particle within the body, wherein the primary abrasiveparticles may be positioned to conduct an initial stage of materialremoval or conduct the majority of material removal compared to thesecondary abrasive particles. In still other instances, the distinctionbetween primary and secondary abrasive particles may pertain to theabrasive nature (e.g., hardness, friability, fracture mechanics, etc.)of the abrasive particles, wherein the abrasive nature of the primaryparticles is typically more robust as compared to the secondary type ofabrasive particles. Some suitable examples of abrasive particles thatmay be considered as a secondary type of abrasive particle includediluent particles, agglomerated particles, unagglomerated particles,naturally occurring materials (e.g., minerals), synthetic materials, anda combination thereof.

In certain instances, the fixed abrasive article 100 can include aparticular content of abrasive particles within the body 101 that mayfacilitate suitable material removal operations. For example, the body101 can include a content of abrasive particles of at least 0.5 vol %for a total volume of the body 101. In other instances, the content ofabrasive particles within the body 101 may be greater, such as at least1 vol %, at least 5 vol %, at least 10 vol %, at least 15 vol %, atleast 20 vol %, at least 25 vol %, at least 30 vol %, at least 35 vol %,at least 40 vol %, or even at least 45 vol %. Still, in anothernon-limiting embodiment, the content of abrasive particles within thebody 101 can be not greater than 60 vol %, such as not greater than 55vol %, not greater than 50 vol %, not greater than 45 vol %, not greaterthan 40 vol %, not greater than 35 vol %, not greater than 30 vol %, notgreater than 25 vol %, not greater than 20 vol %, not greater than 15vol %, or even not greater than 10 vol %. It will be appreciated thatthe content of abrasive particles within the body 101 can be within arange including any of the minimum and maximum percentages noted above,including but not limited to, at least 0.5 vol % to not greater than 50vol %, such as at least 1 vol % and not greater than 45 vol %, or evenwithin a range of at least 5 vol % and not greater than 40 vol %.

Furthermore, the body 101 of the fixed abrasive 100 can include aparticular content of bond material 107 that may facilitate suitableoperation of the fixed abrasive article 100. For example, the body 101can include a content of bond material 107 of at least 0.5 vol % for atotal volume of the body 101. In other embodiments, the content of bondmaterial 107 can be greater, such as at least 1 vol %, at least 5 vol %,at least 10 vol %, at least 20 vol %, at least 30 vol %, at least 40 vol%, at least 50 vol %, at least 60 vol %, or even at least 70 vol %.Still, in a non-limiting embodiment, the body 101 can have a content ofbond material 107 of not greater than about 90 vol %, such as notgreater than 80 vol %, not greater than 70 vol %, not greater than 60vol %, not greater than 50 vol %, not greater than 40 vol %, not greaterthan 30 vol %, not greater than 20 vol %, or even not greater than 10vol %. It will be appreciated that the content of bond material 107within the body 101 can be within a range including any of the minimumand maximum percentages noted above, including for example within arange including at least 0.5 vol % and not greater than 80 vol %, with arange of at least 0.5 vol % and not greater than 50 vol %, or even witha range of at least 1 vol % to not greater than 40 vol %.

In certain instances, the fixed abrasive article can have a body 101including a content of porosity. The porosity can extend throughout atleast a portion of the entire volume of the body 101, and in certaininstances, may extend substantially uniformly throughout the entirevolume of the body 101. For example, the porosity can include closedporosity or open porosity. The closed porosity can be in the form ofdiscrete pores that are isolated from each other by bond material and/orabrasive particles. Such closed porosity may be formed by use of poreformers. In other instances, the porosity may be open porosity, definingan interconnected network of channels extending throughout at least aportion of the three-dimensional volume of the body 101. It will beappreciated that the body 101 may include a combination of closedporosity and open porosity.

In accordance with an embodiment, the fixed abrasive article can have abody 101 including a particular content of porosity that can facilitatesuitable material removal operations. For example, the body 101 can havea porosity of at least 0.5 vol % for a total volume of the body 101. Inother instances, the content of porosity may be greater, such as atleast 1 vol %, at least 5 vol %, at least 8 vol %, at least 10 vol %, atleast 15 vol %, at least 20 vol %, at least 25 vol %, at least 30 vol %,at least 35 vol %, at least 40 vol %, at least 45 vol %, at least 50 vol%, at least 55 vol %, at least 60 vol %, or even at least 65 vol %.Still, in another non-limiting embodiment, the body 101 can include acontent of porosity that is not greater than 80 vol %, such as notgreater than 75 vol %, not greater than 70 vol %, not greater than 65vol %, not greater than 60 vol %, not greater than 55 vol %, not greaterthan 50 vol %, not greater than 45 vol %, not greater than 40 vol %, notgreater 35 vol %, not greater than 30 vol %, not greater than 25 vol %,not greater than 20 vol %, not greater than 15 vol %, not greater than10 vol %, or even not greater than 5 vol %. It will be appreciated thatthe body 101 can have a content of porosity within a range including anyof the minimum and maximum percentages noted above. For example, thebody can have a content of porosity within a range including at least0.5 vol % and not greater than 80 vol %, such as at least 1 vol % andnot greater than 70 vol %, or even at least 5 vol % and not greater than50 vol %.

In accordance with another embodiment, it will be appreciated that thefixed abrasive article 100 can include a body 101 including certainadditives that may facilitate certain grinding operations. For example,the body 101 can include additives such as fillers, grinding aids, poreinducers, hollow materials, catalysts, coupling agents, curants,antistatic agents, suspending agents, anti-loading agents, lubricants,wetting agents, dyes, fillers, viscosity modifiers, dispersants,defoamers, and a combination thereof.

As further illustrated in FIG. 1, the body 101 can have a diameter 183,which may be varied according to the desired material removal operation.The diameter can refer to the maximum diameter of the body, particularlyin those cases where the body 101 has a conical or cup-shaped contour.In accordance with an embodiment, the body 101 can have a diameter 183of at least 20 mm, such as at least 50 mm, at least 80 mm, at least 100mm, at least 120 mm, at least 150 mm, at least 200 mm, at least 400 mm,at least 800 mm, at least 100 cm, at least 200 cm, at least 400 cm, oreven at least 800 cm. In another embodiment, the diameter 183 of thebody can be not greater than 4 m, such as not greater than 2 m. It willbe appreciated the body 101 can have a diameter 183 within a rangeincluding any of the minimum and maximum values noted above.

Moreover, the body can have a particular thickness as defined by theaxis 181 extending along the side surface 103 between the upper surface102 and the bottom surface 104 along the axial axis 180. The body 101can have a thickness 181, which may be an average thickness of the body101, which can be not greater than 1 m, such as not greater than 500 cm,not greater than 200 cm, not greater than 100 cm, not greater than 800mm, not greater than 500 mm, not greater than 200 mm, not greater than100 mm, not greater than 80 mm, not greater than 50 mm, not greater than30 mm, or even not greater than 10 mm. It will be appreciated that thebody may have a thickness 181, including an average thickness, of atleast 1 mm, at least 2 mm, at least 4 mm, at least 8 mm, or even atleast 10 mm. It will be appreciated the body 101 can have a thickness181 within a range including any of the minimum and maximum values notedabove.

In accordance with an embodiment, the body 101 may have a particularrelationship between the diameter 183 and thickness 181, defining aratio of diameter:thickness that may be suitable for certain materialremoval operations. For example, the body 101 can have a ratio ofdiameter:thickness of at least 10:1, such as at least 15:1, at least20:1, at least 50:1, or even at least 100:1. It will be appreciated thatthe body may have a ratio of diameter:thickness of not greater than10,000:1 or not greater than 1000:1.

In certain instances the abrasive particles may have a certain averageparticle size relative to one or more dimensions of the body 101 of thefixed abrasive article, including but not limited to the thickness 181of the body 101. For example, the average particle size (D50), which maybe measured by the longest dimension of the particles, can be less thanthe thickness 181 of the body 101. In particular instances, the abrasiveparticles can have an average particle size that is not greater than 95%of the average thickness of the body, such as not greater than 90%, notgreater than 80%, not greater than 70%, not greater than 60%, notgreater than 50%, not greater than 40%, not greater than 30%, notgreater than 20%, not greater than 10%, not greater than 9%, not greaterthan 8%, not greater than 7%, not greater than 6%, not greater than 5%,not greater than 4%, not greater than 3%, not greater than 2%, or evennot greater than 1% of the average thickness 181 of the body 101. Still,in another non-limiting embodiment, the abrasive particles can have anaverage particle size that is at least 0.001% of the average thicknessof the body 101, such as at least 0.01%, at least 0.1%, at least 1%, atleast 2%, at least 3%, at least 4%, at least 5%, at least 6%, at least7%, at least 8%, at least 9%, at least 10%, at least 11%, at least 12%,at least 15%, at least 20%, or even at least 30% of the averagethickness of the body 101. It will be appreciated that the abrasiveparticles can have a relative average particle size based on the averagethickness of the body within a range including any of the minimum andmaximum percentages noted above, including for example, within a rangeincluding at least 0.001% and not greater than 95%, within a rangeincluding at least 0.01% and not greater than 50%, or even within arange including at least 0.1% and not greater than 20%.

In accordance with an embodiment herein, the fixed abrasive article 100can be a bonded abrasive article including abrasive particles containedwithin the three-dimensional volume of the bond material 107, which canbe distinct from certain other fixed abrasive articles including, forexample, coated abrasive articles, which generally include a singlelayer of abrasive particles contained within a binder, such as a makecoat and/or size coat. Furthermore, coated abrasive articles generallyinclude a backing as a support for the layer of abrasive particles andbinder. By contrast, bonded abrasive articles are generallyself-supporting articles including a three-dimensional volume ofabrasive particles, bond material, and optionally some porosity. Bondedabrasive articles may not necessarily include a substrate, and can beessentially free of a substrate.

The fixed abrasive article 100 may include at least one reinforcingmember 141. In particular instances, the reinforcing material 141 canextend for a majority of the entire width (e.g., the diameter 183) ofthe body 101. However, in other instances, the reinforcing member 141may extend for only a fraction of the entire width (e.g., diameter 183)of the body 101. In certain instances, the reinforcing member 141 may beincluded to add suitable stability to the body for certain materialremoval operations. In accordance with an embodiment, the reinforcingmember 141 can include a material such as a woven material, a nonwovenmaterial, a composite material, a laminated material, a monolithicmaterial, a natural material, a synthetic material, and a combinationthereof. More particularly, in certain instances, the reinforcingmaterial 141 can include a material such as a monocrystalline material,a polycrystalline material, a vitreous material, an amorphous material,a glass (e.g., a glass fiber), a ceramic, a metal, an organic material,an inorganic material, and a combination thereof. In particularinstances, the reinforcing material 141 may include fiberglass, and maybe formed essentially from fiberglass.

In particular instances, the reinforcing material 141 can besubstantially contained within the three-dimensional volume of the body101, more particularly, within the three-dimensional volume of the bondmaterial 107. In certain instances, the reinforcing material 141 mayintersect an exterior surface of the body 101, including, but notlimited to, the upper surface 102, side surface 103, and/or bottomsurface 104. For example, the reinforcing material 141 can intersect theupper surface 102 or bottom surface 104. In at least one embodiment, thereinforcing material 141 may define the upper surface 101 or bottomsurface 104 of the body 101, such that the bond material 107 is disposedbetween one or more reinforcing materials. It will be appreciated thatwhile a single reinforcing member 141 is illustrated in the embodimentof FIG. 1, a plurality of reinforcing members may be provided within thebody 101 in a variety of arrangements and orientations suitable for theintended material removal application.

As further illustrated, the body 101 can include certain axes and planesdefining the three-dimensional volume of the body 101. For example, thebody 101 of the fixed abrasive 100 can include an axial axis 180. Asfurther illustrated along the axial axis 180, the body 101 can include afirst axial plane 131 extending along the axial axis 180 and through aparticular diameter of the body 101 at a particular angular orientation,as designated herein as 0°. As further illustrated, the body 101 caninclude a second axial plane 132 distinct from the first axial plane131. The second axial plane 132 can extend along the axial axis 180 andthrough a diameter of the body 101 at an angular position, as designatedby example herein as 30°. The first and second axial planes 131 and 132of the body 101 may define particular axial collections of abrasiveparticles within the body 101, including for example the axialcollection of abrasive particles 191 associated with the axial plane 131and the axial collection of abrasive particles 192 associated with theaxial plane 132. Furthermore, the axial planes of the body 101 maydefine sectors there between, including for example, sector 184 definedas the region between the axial planes 131 and 132 within the body 101.The sector can include a particular group of abrasive particles that mayfacilitate improved material removal operations. Reference herein tofeatures of portions of abrasive particles within the body, includingabrasive particles within axial planes, will also be relevant to groupsof abrasive particles contained within one or more sectors of the body.

As further illustrated, the body 101 can include a first radial plane121 extending along a plane that is substantially parallel to the uppersurface 102 and/or bottom surface 104 at a particular axial locationalong the axial axis 180. The body can further include a second radialplane 122, which can extend in a substantially parallel manner to theupper surface 102 and/or bottom surface 104 at a particular axiallocation along the axial axis 180. The first radial plane 121 and secondradial plane 122 can be separated from each other within the body 101,and more particularly, the first radial plane 121 and second radialplane 122 can be axially separated from each other. As furtherillustrated, in certain instances, one or more reinforcing members 141may be disposed between the first and second radial planes 121 and 122.As will be described in more detail herein, the first and second radialplanes 121 and 122 may include one or more particular groups of abrasiveparticles, including for example, the group of abrasive particles 106 ofthe first radial plane 121 and the group of abrasive particles 105 ofthe second radial plane 122, which may have certain features relative toeach other that may facilitate improved grinding performance.

The abrasive particles of the embodiments herein can include particulartypes of abrasive particles. For example, the abrasive particles mayinclude shaped abrasive particles and/or elongated abrasive particles,wherein the elongated abrasive particles may include an aspect ratio oflength:width or length:height of at least 1.1:1. Various methods may beutilized to obtain shaped abrasive particles. The particles may beobtained from a commercial source or fabricated. Some suitable processesused to fabricate the shaped abrasive particles can include, but is notlimited to, depositing, printing (e.g., screen-printing), molding,pressing, casting, sectioning, cutting, dicing, punching, pressing,drying, curing, coating, extruding, rolling, and a combination thereof.Similar processes may be utilized to obtain elongated abrasiveparticles. Elongated un-shaped abrasive particles may be formed throughcrushing and sieving techniques.

FIG. 2 includes a perspective view illustration of a shaped abrasiveparticle in accordance with an embodiment. The shaped abrasive particle200 can include a body 201 including a major surface 202, a majorsurface 203, and a side surface 204 extending between the major surfaces202 and 203. As illustrated in FIG. 2, the body 201 of the shapedabrasive particle 200 is a thin-shaped body, wherein the major surfaces202 and 203 are larger than the side surface 204. Moreover, the body 201can include a longitudinal axis 210 extending from a point or corner ofthe shaped abrasive particle 200 to a base (e.g., an edge of the shapedabrasive particle 200 opposite the point or corner) and through themidpoint 250 on the major surface 202. The longitudinal axis 210 candefine the longest dimension of a major surface while also extendingthrough the midpoint 250 of the major surface. The body 201 can furtherinclude a lateral axis 211 defining a width of the body 201 extendinggenerally perpendicular to the longitudinal axis 210 on the same majorsurface 202. Finally, as illustrated, the body 201 can include avertical axis 212, which in the context of thin shaped bodies can definea height (or thickness) of the body 201. For thin-shaped bodies, thelength of the longitudinal axis 210 is equal to or greater than thevertical axis 212. As illustrated, the thickness 212 can extend alongthe side surface 204 between the major surfaces 202 and 203 andperpendicular to the plane defined by the longitudinal axis 210 andlateral axis 211. It will be appreciated that reference herein tolength, width, and height of the abrasive particles may be referenced toaverage values taken from a suitable sampling size of abrasive particlesof a batch.

The shaped abrasive particles can include any of the features of theabrasive particles of the embodiments herein. For example, the shapedabrasive particles can include a crystalline material, and moreparticularly, a polycrystalline material. Notably, the polycrystallinematerial can include abrasive grains. In one embodiment, the body of theabrasive particle, including for example, the body of a shaped abrasiveparticle can be essentially free of an organic material, including forexample, a binder. In at least one embodiment, the abrasive particlescan consist essentially of a polycrystalline material.

Some suitable materials for use as abrasive particles can includenitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond,carbon-containing materials, and a combination thereof. In particularinstances, the abrasive particles can include an oxide compound orcomplex, such as aluminum oxide, zirconium oxide, titanium oxide,yttrium oxide, chromium oxide, strontium oxide, silicon oxide, magnesiumoxide, rare-earth oxides, and a combination thereof. In one particularembodiment, the abrasive particles can include at least 95 wt % aluminafor the total weight of the body. In at least one embodiment, theabrasive particles can consist essentially of alumina. Still, in certaininstances, the abrasive particles can include not greater than 99.5 wt %alumina for the total weight of the body. Moreover, in particularinstances, the shaped abrasive particles can be formed from a seededsol-gel. In at least one embodiment, the abrasive particles of theembodiments herein may be essentially free of iron, rare-earth oxides,and a combination thereof.

The abrasive grains (i.e., crystallites) contained within the body ofthe abrasive particles may have an average grain size that is generallynot greater than about 100 microns. In other embodiments, the averagegrain size can be less, such as not greater than about 80 microns, notgreater than about 50 microns, not greater than about 30 microns, notgreater than about 20 microns, not greater than about 10 microns, notgreater than about 1 micron, not greater than about 0.9 microns, notgreater than about 0.8 microns, not greater than about 0.7 microns, oreven not greater than about 0.6 microns. Still, the average grain sizeof the abrasive grains contained within the body of the abrasiveparticles can be at least about 0.01 microns, such as at least about0.05 microns, at least about 0.06 microns, at least about 0.07 microns,at least about 0.08 microns, at least about 0.09 microns, at least about0.1 microns, at least about 0.12 microns, at least about 0.15 microns,at least about 0.17 microns, at least about 0.2 microns, or even atleast about 0.5 microns. It will be appreciated that the abrasive grainscan have an average grain size within a range between any of the minimumand maximum values noted above.

In accordance with certain embodiments, certain abrasive particles canbe composite articles including at least two different types of grainswithin the body of the abrasive particle. It will be appreciated thatdifferent types of grains are grains having different compositions,different crystallite sizes, and/or different grit sizes with regard toeach other. For example, the body of the abrasive particle can be formedsuch that is includes at least two different types of grains, whereinthe two different types of grains can be nitrides, oxides, carbides,borides, oxynitrides, oxyborides, diamond, and a combination thereof.

In accordance with an embodiment, the abrasive particles can have anaverage particle size, as measured by the largest dimension (i.e.,length) of at least about 100 microns. In fact, the abrasive particlescan have an average particle size of at least about 150 microns, such asat least about 200 microns, at least about 300 microns, at least about400 microns, at least about 500 microns, at least about 600 microns, atleast about 700 microns, at least about 800 microns, or even at leastabout 900 microns. Still, the abrasive particles of the embodimentsherein can have an average particle size that is not greater than about5 mm, such as not greater than about 3 mm, not greater than about 2 mm,or even not greater than about 1.5 mm. It will be appreciated that theabrasive particles can have an average particle size within a rangebetween any of the minimum and maximum values noted above.

FIG. 2 includes an illustration of a shaped abrasive particle having atwo-dimensional shape as defined by the planes of the major surfaces 202or 203, each of which has a generally triangular two-dimensional shape.It will be appreciated that the shaped abrasive particles of theembodiments herein are not so limited and can include othertwo-dimensional shapes. For example, the shaped abrasive particles ofthe embodiment herein can include particles having a body with atwo-dimensional shape as defined by a major surface of the body from thegroup of shapes including polygons, irregular polygons, irregularpolygons including arcuate or curved sides or portions of sides,ellipsoids, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, Kanji characters, complexshapes having a combination of polygons shapes, star shapes, and acombination thereof.

FIG. 3A includes a perspective view illustration of a shaped abrasiveparticle according to an embodiment. Notably, the shaped abrasiveparticle 300 can include a body 301 including a surface 302 and asurface 303, which may be referred to as end surfaces 302 and 303. Thebody can further include surfaces 304, 305, 306, 307 extending betweenand coupled to the end surfaces 302 and 303. The shaped abrasiveparticle of FIG. 3A is an elongated shaped abrasive particle having alongitudinal axis 310 that extends along the surface 305 and through themidpoint 340 between the end surfaces 302 and 303. It will beappreciated that the surface 305 is selected for illustrating thelongitudinal axis 310, because the body 301 has a generally squarecross-sectional contour as defined by the end surfaces 302 and 303. Assuch, the surfaces 304, 305, 306, and 307 have approximately the samesize relative to each other. However, in the context of other elongatedabrasive particles wherein the surfaces 302 and 303 define a differentshape, for example a rectangular shape, wherein one of the surfaces 304,305, 306, and 307 may be larger relative to the others, the largest ofthose surfaces defines the major surface and, therefore, thelongitudinal axis would extend along the largest of those surfaces. Asfurther illustrated, the body 301 can include a lateral axis 311extending perpendicular to the longitudinal axis 310 within the sameplane defined by the surface 305. As further illustrated, the body 301can further include a vertical axis 312 defining a height of theabrasive particle, wherein the vertical axis 312 extends in a directionperpendicular to the plane defined by the longitudinal axis 310 andlateral axis 311 of the surface 305.

It will be appreciated that, like the thin shaped abrasive particle ofFIG. 2, the elongated shaped abrasive particle of FIG. 3A can havevarious two-dimensional shapes such as those defined with respect to theshaped abrasive particle of FIG. 2. The two-dimensional shape of thebody 301 can be defined by the shape of the perimeter of the endsurfaces 302 and 303. The elongated shaped abrasive particle 300 canhave any of the attributes of the shaped abrasive particles of theembodiments herein.

FIG. 3B includes an illustration of an elongated particle, which is nota shaped abrasive particle. Shaped abrasive particles may be formedthrough particular processes, including molding, printing, casting,extrusion, and the like. Shaped abrasive particles are formed such thateach particle has substantially the same arrangement of surfaces andedges relative to each other. For example, a group of shaped abrasiveparticles generally have the same arrangement and orientation and ortwo-dimensional shape of the surfaces and edges relative to each other.As such, the shaped abrasive particles have a high shape fidelity andconsistency in the arrangement and orientation of the surfaces and edgesrelative to each other. By contrast, non-shaped abrasive particles canbe formed through different processes and have different shapeattributes. For example, crushed grains are typically formed by acomminution process wherein a mass of material is formed and thencrushed and sieved to obtain abrasive particles of a certain size.However, a non-shaped abrasive particle will have a generally randomarrangement of the surfaces and edges, and generally will lack anyrecognizable two-dimensional or three-dimensional shape in thearrangement of the surfaces and edges. Moreover, the non-shaped abrasiveparticles do not necessarily have a consistent shape with respect toeach other and therefore have a significantly lower shape fidelitycompared to shaped abrasive particles. The non-shaped abrasive particlesgenerally are defined by a random arrangement of surfaces and edges withrespect to each other.

As further illustrated in FIG. 3B, the elongated abrasive article can bea non-shaped abrasive particle having a body 351 and a longitudinal axis352 defining the longest dimension of the particle, a lateral axis 353extending perpendicular to the longitudinal axis 352 and defining awidth of the particle. Furthermore, the elongated abrasive particle mayhave a height (or thickness) as defined by the vertical axis 354 whichcan extend generally perpendicular to a plane defined by the combinationof the longitudinal axis 352 and lateral axis 353. As furtherillustrated, the body 351 of the elongated, non-shaped abrasive particlecan have a generally random arrangement of edges 355 extending along theexterior surface of the body 351.

As will be appreciated, the elongated abrasive particle can have alength defined by longitudinal axis 352, a width defined by the lateralaxis 353, and a vertical axis 354 defining a height. As will beappreciated, the body 351 can have a primary aspect ratio oflength:width such that the length is greater than the width.Furthermore, the length of the body 351 can be greater than or equal tothe height. Finally, the width of the body 351 can be greater than orequal to the height 354. In accordance with an embodiment, the primaryaspect ratio of length:width can be at least 1.1:1, at least 1.2:1, atleast 1.5:1, at least 1.8:1, at least 2:1, at least 3:1, at least 4:1,at least 5:1, at least 6:1, or even at least 10:1. In anothernon-limiting embodiment, the body 351 of the elongated abrasive particlecan have a primary aspect ratio of length:width of not greater than100:1, not greater than 50:1, not greater than 10:1, not greater than6:1, not greater than 5:1, not greater than 4:1, not greater than 3:1,or even not greater than 2:1. It will be appreciated that the primaryaspect ratio of the body 351 can be with a range including any of theminimum and maximum ratios noted above.

Furthermore, the body 351 of the elongated abrasive particle 350 caninclude a secondary aspect ratio of width:height that can be at least1.1:1, such as at least 1.2:1, at least 1.5:1, at least 1.8:1, at least2:1, at least 3:1, at least 4:1, at least 5:1, at least 8:1, or even atleast 10:1. Still, in another non-limiting embodiment, the secondaryaspect ratio width:height of the body 351 can be not greater than 100:1,such as not greater than 50:1, not greater than 10:1, not greater than8:1, not greater than 6:1, not greater than 5:1, not greater than 4:1,not greater than 3:1, or even not greater than 2:1. It will beappreciated the secondary aspect ratio of width:height can be with arange including any of the minimum and maximum ratios of above.

In another embodiment, the body 351 of the elongated abrasive particle350 can have a tertiary aspect ratio of length:height that can be atleast 1.1:1, such as at least 1.2:1, at least 1.5:1, at least 1.8:1, atleast 2:1, at least 3:1, at least 4:1, at least 5:1, at least 8:1, oreven at least 10:1. Still, in another non-limiting embodiment, thetertiary aspect ratio length:height of the body 351 can be not greaterthan 100:1, such as not greater than 50:1, not greater than 10:1, notgreater than 8:1, not greater than 6:1, not greater than 5:1, notgreater than 4:1, or even not greater than 3:1. It will be appreciatedthat the tertiary aspect ratio of the body 351 can be within a rangeincluding any of the minimum and maximum ratios and above.

The elongated abrasive particle 350 can have certain attributes of theother abrasive particles described in the embodiments herein including,but not limited to, composition, microstructural features (e.g., averagegrain size), hardness, porosity, and the like.

FIG. 4A includes a top view illustration of a shaped abrasive particleaccording to an embodiment. In particular, the shaped abrasive particle400 can include a body 401 having the features of other shaped abrasiveparticles of embodiments herein, including an upper major surface 403and a bottom major surface (not shown) opposite the upper major surface403. The upper major surface 403 and the bottom major surface can beseparated from each other by at least one side surface 405, which mayinclude one or more discrete side surface portions, including forexample, a first portion 406 of the side surface 405, a second portion407 of the side surface 405, and a third portion 408 of the side surface405. In particular, the first portion 406 of the side surface 405 canextend between a first corner 409 and a second corner 410. The secondportion 407 of the side surface 405 can extend between the second corner410 and a third corner 411. Notably, the second corner 410 can be anexternal corner joining two portions of the side surface 405. The secondcorner 410 and a third corner 411, which is also an external corner, areadjacent to each other and have no other external corners disposedbetween them. Also, the third portion 408 of the side surface 405 canextend between the third corner 411 and the first corner 409, both ofwhich are external corners that are adjacent to each other and have noother external corners disposed between them.

As illustrated, the body 401 can include a first portion 406 including afirst curved section 442 disposed between a first linear section 441 anda second linear section 443 and between the external corners 409 and410. The second portion 407 is separated from the first portion 406 ofthe side surface 405 by the external corner 410. The second portion 407of the side surface 405 can include a second curved section 452 joininga third linear section 451 and a fourth linear section 453. Furthermore,the body 401 can include a third portion 408 separated from the firstportion 406 of the side surface 405 by the external corner 409 andseparated from the second portion 407 by the external corner 411. Thethird portion 408 of the side surface 405 can include a third curvedsection 462 joining a fifth linear section 461 and a sixth linearsection 463.

FIG. 4B includes a top view of a shaped abrasive particle 430 accordingto an embodiment. The tip sharpness of a shaped abrasive particle, whichmay be an average tip sharpness, may be measured by determining theradius of a best fit circle on an external corner 431 of the body 432.For example, a top view of the upper major surface 433 of the body 432is provided. At an external corner 431, a best fit circle is overlaid onthe image of the body 432 of the shaped abrasive particle 430, and theradius of the best fit circle relative to the curvature of the externalcorner 431 defines the value of tip sharpness for the external corner431. The measurement may be recreated for each external corner of thebody 432 to determine the average individual tip sharpness for a singleshaped abrasive particle 430. Moreover, the measurement may be recreatedon a suitable sample size of shaped abrasive particles of a batch ofshaped abrasive particles to derive the average batch tip sharpness. Anysuitable computer program, such as ImageJ may be used in conjunctionwith an image (e.g., SEM image or light microscope image) of suitablemagnification to accurately measure the best fit circle and the tipsharpness.

The shaped abrasive particles of the embodiments herein may have aparticular tip sharpness that may facilitate suitable performance in thefixed abrasive articles of the embodiments herein. For example, the bodyof a shaped abrasive particle can have a tip sharpness of not greaterthan 80 microns, such as not greater than 70 microns, not greater than60 microns, not greater than 50 microns, not greater than 40 microns,not greater than 30 microns, not greater than 20 microns, or even notgreater than 10 microns. In yet another non-limiting embodiment, the tipsharpness can be at least 2 microns, such as at least 4 microns, atleast 10 microns, at least 20 microns, at least 30 microns, at least 40microns, at least 50 microns, at least 60 microns, or even at least 70microns. It will be appreciated that the body can have a tip sharpnesswithin a range between any of the minimum and maximum values notedabove.

Another grain feature of shaped abrasive particles is the Shape Index.The Shape Index of a body of a shaped abrasive particle can be describedas a value of an outer radius of a best-fit outer circle superimposed onthe body, as viewed in two dimensions of a plane of length and width ofthe body (e.g., the upper major surface or the bottom major surface),compared to an inner radius of the largest best-fit inner circle thatfits entirely within the body, as viewed in the same plane of length andwidth. For example, turning to FIG. 4C, a shaped abrasive particle isprovided with two circles superimposed on the illustration todemonstrate the calculation of Shape Index. A first circle issuperimposed on the body 470 of the shaped abrasive particle, which is abest-fit outer circle representing the smallest circle that can be usedto fit the entire perimeter of the body 470 within its boundaries. Theouter circle has a radius (Ro). For shapes such as that illustrated inFIG. 4C, the outer circle may intersect the perimeter of the body ateach of the three external corners. However, it will be appreciated thatfor certain irregular or complex shapes, the body may not fit uniformlywithin the circle such that each of the corners intersect the circle atequal intervals, but a best-fit, outer circle still may be formed. Anysuitable computer program, such as ImageJ, may be used in conjunctionwith an image of suitable magnification (e.g., SEM image or lightmicroscope image) to create the outer circle and measure the radius(Ro).

A second, inner circle can be superimposed on the body 470, asillustrated in FIG. 4C, which is a best fit circle representing thelargest circle that can be placed entirely within the perimeter of thebody 470 as viewed in the plane of the length and width of the body 470.The inner circle can have a radius (Ri). It will be appreciated that forcertain irregular or complex shapes, the inner circle may not fituniformly within the body such that the perimeter of the circle contactsportions of the body at equal intervals, such as shown for the shape ofFIG. 4C. However, a best-fit, inner circle still may be formed. Anysuitable computer program, such as ImageJ, may be used in conjunctionwith an image of suitable magnification (e.g., SEM image or lightmicroscope image) to create the inner circle and measure the radius(Ri).

The Shape Index can be calculated by dividing the outer radius by theinner radius (i.e., Shape Index=Ri/Ro). For example, the body 470 of theshaped abrasive particle has a Shape Index of approximately 0.35.Moreover, an equilateral triangle generally has a Shape Index ofapproximately 0.5, while other polygons, such as a hexagon or pentagon,have Shape Index values greater than 0.5. In accordance with anembodiment, the shaped abrasive particles herein can have a Shape Indexof at least 0.02, such as at least 0.05, at least 0.10, at least 0.15,at least 0.20, at least 0.25, at least 0.30, at least 0.35, at least0.40, at least 0.45, at least about 0.5, at least about 0.55, at least0.60, at least 0.65, at least 0.70, at least 0.75, at least 0.80, atleast 0.85, at least 0.90, or at least 0.95. Still, in anothernon-limiting embodiment, the shaped abrasive particle can have a ShapeIndex of not greater than 1, such as not greater than 0.98, not greaterthan 0.95, not greater than 0.90, not greater than 0.85, not greaterthan 0.80, not greater than 0.75, not greater than 0.70, not greaterthan 0.65, not greater than 0.60, not greater than 0.55, not greaterthan 0.50, not greater than 0.45, not greater than 0.40, not greaterthan 0.35, not greater than 0.30, not greater than 0.25, not greaterthan 0.20, not greater than 0.15, not greater than 0.10, not greaterthan 0.05, or not greater than 0.02. It will be appreciated that theshaped abrasive particles can have a Shape Index within a range betweenany of the minimum and maximum values noted above.

FIG. 4D includes a top view of a shaped abrasive particle according toanother embodiment. The shaped abrasive particle 480 can have a body 481having the features of other shaped abrasive particles of embodimentsherein, including an upper major surface 483 and a bottom major surface(not shown) opposite the upper major surface 483. The upper majorsurface 483 and the bottom major surface can be separated from eachother by at least one side surface 484, which may include one or morediscrete side surface sections. According to one embodiment, the body481 can be defined as an irregular hexagon, wherein the body has ahexagonal (i.e., six-sided) two dimensional shape as viewed in the planeof a length and a width of the body 481, and wherein at least two of thesides, such as sides 485 and 486, have a different length with respectto each other. Notably, the length of the sides is understood herein torefer to the width of the body 481 and the length of the body is thegreatest dimension extending through the midpoint of the body 481.Moreover, as illustrated, none of the sides are parallel to each other.And furthermore, while not illustrated, any of the sides may have acurvature to them, including a concave curvature wherein the sides maycurve inwards toward the interior of the body 481.

In accordance with an embodiment, the abrasive particles, which caninclude shaped abrasive particles and/or elongated abrasive particles,can be placed within the body 101 of the fixed abrasive article 100depicted in FIG. 1 such that the abrasive particles have a predeterminedposition and/or predetermined three-axis orientation. FIG. 5A includes atop-down illustration of a first group of abrasive particles 545 withina radial plane of the body 101 (as depicted in FIG. 1). As illustrated,the first group 545 can include a plurality of abrasive particles,including abrasive particles 502, 503, 504, 505, and 506 (502-506). Thefirst group 545 may further include abrasive particles 522, 523, 524,525, 526 (522-526). Unlike conventional fixed abrasive articles,including conventional bonded abrasive articles, where the abrasiveparticles are randomly positioned and randomly oriented within thevolume of the body, the fixed abrasive articles of the embodimentsherein include abrasive particles in a predetermined position within thethree-dimensional volume of the body 101. Furthermore, the abrasiveparticles of the embodiments herein can be placed within thethree-dimensional volume of the body with a predetermined three-axisorientation. The provision of the abrasive particles in a predeterminedposition and/or predetermined three-axis orientation may facilitateimproved material removal performance of the fixed abrasive articlecompared to conventional fixed abrasive articles having abrasiveparticles randomly positioned and oriented within the body.

The first group of abrasive particles 545 within a radial plane (e.g.,the radial plane 122 depicted in FIG. 1) can each have a predeterminedthree-axis orientation, including a predetermined rotationalorientation, relative to the side surface 103 of the body 101. Forexample, the shaped abrasive particle 502 can have a longitudinal axis511. The longitudinal axis 511 extends from a point or corner of theshaped abrasive particle 502 through the midpoint of a major surface ofthe shaped abrasive particle 502. In an embodiment and as shown in FIG.5A, the longitudinal axis 511 can be substantially aligned with a radialaxis 512 of the body 101. The radial axis 512 is a radius of the body101 within the radial plane 122 that also extends through the midpointof the major surface of the particle defining the longitudinal axis 511of the particle. Furthermore, the radial axis 512 is substantiallyperpendicular to the side surface 103 to which the abrasive particle ismost closely positioned. A predetermined rotational orientation angle isthe angle between the longitudinal axis 511 of the shaped abrasiveparticle (or elongated particle) and the radial axis 512 in a planedefined by a length and a width of the shaped abrasive particle 502.More specifically, the predetermined rotational orientation angle ismeasured at the point along the longitudinal axis 511 closest to theside surface 103. Therefore, the predetermined rotational orientationangle of the shaped abrasive particle 502 relative to the side surface103 in FIG. 5A is substantially 0°. In accordance with an embodiment, atleast a portion of the abrasive particles within the fixed abrasivearticle 100 can have a predetermined rotational orientation angle thatis less than 90°. For example, the average predetermined rotationalorientation angle for a portion of the abrasive particles can be notgreater than 90°, such as not greater than 80°, not greater than 70°,not greater than 60°, not greater than 50°, not greater than 40°, notgreater than 30°, not greater than 20°, not greater than 10°, or notgreater than 5°. Still, in another non-limiting embodiment, the averagepredetermined rotational orientation angle for a portion of the abrasiveparticles within the body 101 can be at least 0.1°, such as at least 1°,at least 3°, at least 5°, at least 10°, at least 20°, at least 30°, atleast 40°, or even at least 50°. It will be appreciated that the averagepredetermined rotational orientation angle may be controlled tofacilitate improved grinding performance of the fixed abrasive article.Furthermore, the average predetermined rotational orientation angle fora portion of the abrasive particles in the body 101 can be within arange including any of the minimum and maximum angles noted above.

For any of the embodiments herein, reference to a portion of theabrasive particles having a predetermined rotational orientation anglecan include at least a content of abrasive particles, particularlyshaped abrasive particles and/or elongated abrasive particles, which canbe distinct from conventional articles having a random orientation ofthe abrasive particles. For example, a portion of abrasive particles inthe body can include at least 10%, such as at least 20%, at least 30%,at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, oreven at least 90% of the total abrasive particles within the body 101.In accordance with a particular embodiment, essentially all of theabrasive particles, including only the shaped abrasive particles and/orelongated abrasive particles, can have a predetermined rotationalorientation angle within a range including any of the minimum andmaximum values noted above. Moreover, as will be understood in light ofthe entire disclosure and embodiments herein, a portion of abrasiveparticles within the body 101 can include a group of abrasive particles(e.g., a first group of abrasive particles in a radial plane or in asector), a radial set of abrasive particles, an axial collection ofabrasive particles, and a combination thereof.

Furthermore, at least a portion of the abrasive particles, including theshaped abrasive particles and/or elongated abrasive particles within thebody 101, may have a standard deviation of predetermined rotationalorientation angle. A low standard deviation indicates a high degree ofcontrol of the predetermined rotational orientation angle for thatportion of the abrasive particles having the predetermined rotationalorientation angle within the body 101. For example, in accordance withan embodiment, the portion of abrasive particles within the body 101having a predetermined rotational orientation angle can have a standarddeviation of that predetermined rotational orientation angle of notgreater than 20 degrees, not greater than 18 degrees, not greater than16 degrees, not greater than 14 degrees, not greater than 12 degrees,not greater than 10 degrees, not greater than 9 degrees, not greaterthan 8 degrees, not greater than 7 degrees, or even not greater than 6degrees. Still, in at least one non-limiting embodiment, the portion ofthe abrasive particles in the body having a predetermined rotationalorientation angle can have a standard deviation of that predeterminedrotational orientation angle of at least 0.01 degrees, such as at least0.1 degrees, or even at least 1 degree. It will be appreciated that thestandard deviation of the predetermined rotational orientation angle canbe within a range including any of the minimum maximum values notedabove. Reference herein to a portion of the abrasive particles withinthe body 101 having a standard deviation predetermined rotationorientation angle can be reference to a portion as described herein.

Referring briefly to FIG. 5B, an illustration of a shaped abrasiveparticle contained in a body of a fixed abrasive in a predeterminedthree-axis orientation is provided. Reference to a predeterminedthree-axis orientation includes the control of the three axes definingthe shaped abrasive particle 502 (including the longitudinal axis 585extending through a midpoint 584 of a first major surface 581, thelateral axis 586, and the vertical axis 587) within the body 101 and,more particularly, relative to a side surface 103 of the body 101. Inparticular, the shaped abrasive particle 502 can be lying flat withinthe body relative to a major surface of the body 101. That is, theshaped abrasive particle 502 can have the first major surface 581, asecond major surface 582, and a side surface 583 extending between thefirst and second major surfaces 581 and 582. The longitudinal axis 585,extending between a tip or corner of the shaped abrasive particle 502and a base or edge opposite that tip/corner and also extending throughthe midpoint 584, can extend substantially parallel to a major surfaceof the body 101, such as the upper surface 102 and/or bottom surface104. Moreover, the longitudinal axis 585 can extend substantiallyperpendicular to the side surface 103 of the body 101 such that, at thepoint where the radial axis 512 intersects the side surface 103, theangle formed by the longitudinal axis 585 and the side surface 103 issubstantially orthogonal when viewed top-down in the plane of a majorsurface of the body 101. This may be particularly advantageous for fixedabrasive articles where the side surface 103 is configured to conductthe primary material removal operations. As such, it may be particularlysuitable for the shaped abrasive particles and/or elongated abrasiveparticles to have a three-axis orientation, including a predeterminedrotational orientation, relative to the side surface 103 of the body101.

As further illustrated in FIG. 5B, the lateral axis 586 defining a widthof the shaped abrasive particle 502 also can extend substantiallyparallel to a major surface of the body 101, such as the upper surface102 and/or bottom surface 104. Moreover, in some embodiments, thelateral axis 586 can extend substantially parallel to a tangent 588 ofthe side surface 103 of the body 101 at the point where the radial axis512 intersects the side surface 103.

As further illustrated in FIG. 5B, the vertical axis 587 defining aheight of the shaped abrasive particle 502 can extend substantiallyperpendicular to a major surface of the body 101, such as the uppersurface 102 and/or bottom surface 104. Moreover, in some embodiments,the vertical axis 587 can extend substantially parallel to a tangent 589of the side surface 103 of the body 101 at the point where the radialaxis 512 intersects the side surface 103.

Referring again to FIG. 5A, the first group of abrasive particles 545can include a first portion of abrasive particles having substantiallythe same predetermined three-axis orientation relative to the sidesurface 103 of the body 101. For example, the abrasive particles502-506, which are shaped abrasive particles whose major surfaces have atriangular two-dimensional shape, can have substantially the samethree-axis orientation relative to the side surface 103. Moreparticularly, the abrasive particles 502-506 can have substantially thesame predetermined rotational orientation angle relative to the sidesurface 103. As illustrated in the embodiment of FIG. 5A, the abrasiveparticle 502 has a longitudinal axis 511 that is substantially alignedwith the radial axis 512, thereby defining a predetermined rotationalorientation angle of approximately 0° at the point where thelongitudinal axis 511 is closest to the side surface 103. Likewise, theabrasive particle 503 includes a longitudinal axis 513 that issubstantially aligned with the radial axis 514. Therefore, the abrasiveparticle 503 also has a predetermined rotational orientation angle ofapproximately 0° at the point where the longitudinal axis 513 is closestto the side surface 103. Furthermore, abrasive particle 504 has alongitudinal axis 515 that is substantially aligned with radial axis516. Therefore, the abrasive particle 504 has a predetermined rotationalorientation angle of approximately 0° at the point where thelongitudinal axis 515 is closest to the side surface 103. The abrasiveparticle 505 has a longitudinal axis 517 that is substantially alignedwith the radial axis 518, also defining a predetermined rotationalorientation angle of approximately 0°. Moreover, the abrasive particle506 has a longitudinal axis 519 substantially aligned with the radialaxis 520, thereby defining a predetermined rotational orientation angleof approximately 0°. Accordingly, the abrasive particles 502-506 canhave substantially the same predetermined rotational orientationrelative to the side surface 103 as defined by the respectivepredetermined rotational orientation angles associated with each of theabrasive particles 502-506. Moreover, it will be appreciated that eachof the abrasive particles 502-506 have substantially the sameorientation of their lateral axes and vertical axes relative to thecorresponding radial axes 512, 514, 516, 518, and 520 and the sidesurface 103. Moreover, while the shaped abrasive particles of FIG. 5Aare illustrated as having generally triangular two-dimensional shapes,other types of shaped abrasive particles and/or elongated abrasiveparticles may be utilized.

As further illustrated in FIG. 5A, at least a portion of the abrasiveparticles within the body 101 can be arranged in a controlleddistribution relative to each other. A controlled distribution can bedefined by a combination of predetermined positions within the body thatare purposefully selected to be occupied by the abrasive particles. Acontrolled distribution can include a pattern, such that thepredetermined positions can define a two-dimensional array. An array caninclude have short range order defined by a unit of abrasive particles.An array may also be a pattern having long range order, includingregular and repetitive units linked together, such that the arrangementmay be symmetrical and/or predictable. An array may have an order thatcan be predicted by a mathematical formula. It will be appreciated thattwo-dimensional arrays can be formed in the shape of polygons, ellipsis,ornamental indicia, product indicia, or other designs. A controlled orpredetermined distribution can also include a non-shadowing arrangement.A non-shadowing arrangement may include a controlled, non-uniformdistribution, a controlled uniform distribution, and a combinationthereof. In particular instances, a non-shadowing arrangement mayinclude a radial pattern, a spiral pattern, a phyllotactic pattern, anasymmetric pattern, a self-avoiding random distribution, and acombination thereof. In other instances, a non-shadowing arrangement caninclude an intentional staggering of two or more particles relative toone another (i.e., an intentional staggering of two or morepredetermined positions and/or predetermined rotational orientations),as discussed more fully with respect to FIG. 8.

According to one embodiment, the first group 545 of abrasive particlesare arranged in a controlled distribution relative to each other withina radial plane (e.g., the radial plane 122 depicted in FIG. 1). As willbe appreciated, each of the abrasive particles within the first group545 can have substantially the same axial position within the body 101such that each of the abrasive particles are positioned within theradial plane 122. The abrasive particles contained within the firstgroup 545 may have different radial positions with respect to eachother. For example, the abrasive particles 522-526 can have the sameaxial position relative to one another and a different radial positionrelative to the abrasive particles 502-506. It will be appreciated thatreference to the radial position can be referenced to the position ofthe abrasive particles along a radial axis including, for example,radial axes 512-520.

Referring to FIG. 5C, a top-down view of a radial plane of abrasiveparticles within a body of a fixed abrasive article is illustrated. Asshown, the abrasive particles within the radial plane of the body can bearranged in various controlled distributions with respect to each other.For example, the abrasive particles of the first group 591 can bearranged in a controlled distribution that has a generally rectangularpattern, such that the smallest unit 595 of abrasive particles defines arectangle. As will be appreciated and as illustrated, other types ofcontrolled distributions may be utilized. In certain instances,different groups of abrasive particles within the radial plane candefine different controlled distributions. For example, as illustrated,the abrasive particles of the group 592 may be arranged in a differentcontrolled distribution relative to those abrasive particles of thefirst group 591. Likewise, the abrasive particles of the group 593 canbe arranged in yet another controlled distribution relative to groups591 and 592. Finally, the abrasive particles of the group 594 may have adifferent controlled distribution relative to the abrasive particles ofthe groups 593, 592, and 591. The controlled distributions provided inFIG. 5C are merely illustrative and are non-limiting. Various controlleddistributions may be utilized to improve the grinding performance of thefixed abrasive article.

The predetermined position of the abrasive particles relative to eachother can define the controlled distribution. For example, referringagain to FIG. 5A, the abrasive particles 502-506 can be spaced apartfrom each other in a predetermined manner, which may facilitate improvedmaterial removal operations. For example, as illustrated, the abrasiveparticle 502 is spaced apart from the abrasive particle 503 by a spacingdistance 551 defined as the smallest distance between the abrasiveparticles 502 and 503. Moreover, the abrasive particle 503 is spacedapart from the abrasive particle 504 by a spacing distance 552, theabrasive particle 504 is spaced apart from the abrasive particle 505 bya spacing distance 553, and the abrasive particle 505 is spaced apartfrom the abrasive particle 506 by a spacing distance 554. According toan embodiment, at least a portion of the abrasive particles within thebody can have substantially the same spacing distance, including forexample, the spacing distances 551-554 between the abrasive particles502-504. The portion can include any portion of abrasive particles asdescribed in embodiments herein.

Furthermore, a suitable spacing distance between particles may be basedon the average particle size (PSa) of the portion of abrasive particles,wherein the average particle size of shaped abrasive particles is basedon the length of the particles and the spacing distance can be anaverage spacing distance between the abrasive particles of the portion.For example, the spacing distance between a portion of the abrasiveparticles within the body can be not greater than 10 (PSa), such as notgreater than 9 (PSa), not greater than 8 (PSa), not greater than 7(PSa), such as not greater than 6 (PSa), not greater than 5 (PSa), notgreater than 4 (PSa), such as not greater than 3 (PSa), not greater than2 (PSa), not greater than 1 (PSa), such as not greater than 0.8 (PSa),not greater than 0.5 (PSa), not greater than 0.4 (PSa), or even notgreater than 0.2 (PSa). In at least one embodiment, the spacing distancefor a portion of abrasive particles can be 0, such that the abrasiveparticles are in contact with each other, which may be particularlydesirable for certain material removal operations. Still, in anothernon-limiting embodiment, the spacing distance can be at least 0.1 (PSa),at least about 0.2 (PSa), at least 0.5 (PSa), at least 0.8 (PSa), atleast 1 (PSa), at least 2 (PSa), or even at least 3 (PSa). It will beappreciated that the spacing distance can be within a range includingany of the minimum and maximum values noted above.

In still another embodiment, the portion of abrasive particles can havea particularly low standard deviation of spacing distance, which candemonstrate the level of control in the predetermined positioning of theabrasive particles within the body. For example, the standard deviationof the spacing distance can be not greater than 2 (PSa), such as notgreater than 1.8 (PSa), not greater than 1.5 (PSa), not greater than 1.2(PSa), such as not greater than 1 (PSa), not greater than 0.8 (PSa), notgreater than 0.7 (PSa), not greater than 0.6 (PSa), not greater than 0.5(PSa), not greater than 0.4 (PSa), not greater than 0.3 (PSa), notgreater than 0.2 (PSa), not greater than 0.1 (PSa), not greater than0.08 (PSa), not greater than 0.06 (PSa), not greater than 0.04 (PSa),not greater than 0.03 (PSa), or even not greater than 0.02 (PSa). Still,in at least one non-limiting embodiment, the standard deviation of thespacing distance for a portion of the abrasive particles in the body canbe at least 0.0001 (PSa), such as at least 0.001 (PSa) or even at least0.01 (PSa). It will be appreciated that the standard deviation ofspacing distance can be within a range including any of the minimum andmaximum values noted above.

Reference herein to the spacing distance and standard deviation ofspacing distance can include reference to the spacing between abrasiveparticles in the same radial plane, the spacing between abrasiveparticles in different radial planes, the spacing between abrasiveparticles in the same axial collection (i.e., within the same axialplane), the spacing between abrasive particles in different axialcollections (i.e., within different axial planes), the spacing betweenabrasive particles in a radial set, the spacing between abrasiveparticles between different radial sets, the spacing between abrasiveparticles within a sector, and the spacing between abrasive particles indifferent sectors.

According to an embodiment, the abrasive particles of the first group545 can have at least one abrasive characteristic that is substantiallythe same with respect to each other. Abrasive characteristics caninclude hardness, composition, average particle size, average grainsize, fracture toughness, two-dimensional shape, tip sharpness, tipangle, aspect ratio, and a combination thereof. For example, asillustrated in FIG. 5A, the abrasive particles of the first group 545can have substantially the same two-dimensional shape (i.e., triangulartwo-dimensional shape) with respect to each other. However, it will alsobe appreciated that at least a portion of the abrasive particles withinthe first group 545 may have at least one abrasive characteristic thatis distinct from each other. Moreover, as also illustrated in FIG. 5A,the abrasive particles of the first group 545 may have at least onecharacteristic such as an orientation (e.g., a predetermined rotationalorientation) and/or position that is distinct from each other. Forexample, in the illustrated embodiment of FIG. 5A, each of the abrasiveparticles 502-506 have a substantially different predeterminedrotational rotation angle relative to each of the abrasive particles522-526. As will be appreciated, this need not necessarily be the case,and at least a portion of the shaped abrasive particles of the firstgroup, such as the abrasive articles 502-506, can have substantially thesame orientation characteristics with respect to each other, includingfor example, substantially the same predetermined rotational orientationangle.

As further illustrated in FIG. 5A, the first group of abrasive particles545 may include a first radial set 501 of abrasive particles spaced at afirst radial distance from the center of the body 101 (e.g., from theaxial axis 180). That is, the abrasive particles 502-506 may define afirst radial set 501 of abrasive particles having substantially the sameradial distance along their respective radial axes 512-520 within thebody 101. Accordingly, each of the abrasive particles of the firstradial set 501 may also be substantially the same distance from the sidesurface 103. As noted herein, the abrasive particles 502-506 of thefirst radial set 501 can have substantially the same predeterminedrotational orientation relative to each other. Moreover, each of theabrasive particles 502-506 of the first radial set 501 can havesubstantially the same predetermined rotational orientation relative tothe side surface 103 of the body 101, including a predeterminedthree-axis orientation and a predetermined rotational orientationrelative to the side surface 103 of the body 101. In accordance with anembodiment, the abrasive particles 502-506 of the first radial set 501may have substantially the same axial position with respect to eachother within the body, such that they are within the same radial plane122. Furthermore, it will be appreciated that each of the abrasiveparticles 502-506 of the first radial set 501 may have at least oneabrasive characteristic that is substantially the same with respect toeach other, including for example abrasive characteristic of hardness,composition, average particle size, average grain size, fracturetoughness, two-dimensional shape, tip sharpness, tip angle, aspectratio, and a combination thereof.

As further illustrated, the first group of abrasive particles 545 caninclude a second radial set 521 of abrasive particles 522-526 that canbe spaced at a particular radial distance from the center of the body(e.g., from the axial axis 180). That is, the abrasive particles 522-526may define a second radial set 502 of abrasive particles havingsubstantially the same radial distance along their respective radialaxes 512-520 within the body 101. Notably, the radial distance of theabrasive particles 522-526 can be measured as the distance from thecenter of body along their respective radial axes 512-520. Moreover,each of the abrasive particles 522-526 of the second radial set 521 maybe spaced at substantially the same distance from the side surface 103of the body 101. Moreover, the abrasive particles 522-526 of the secondradial set can be spaced at a second radial distance from the center ofthe body that is different than the first radial distance of theabrasive particles 502-506 of the first radial set 501. For example, asillustrated in FIG. 5A, the abrasive particles 502-506 of the firstradial set 501 can be spaced at a distance further from the center ofthe body and closer to the side surface 103 of the body 101 along theirrespective radial axes 512-520 as compared to the abrasive particles522-526 of the second radial set 521, which are closer to the center ofthe body 101 as compared to the abrasive particles 502-506. Moreover, asprovided in the illustrated embodiment, the abrasive particles 522-526of the second radial set 521 are further away from the side surface 103as compared to the abrasive particles 502-506 of the first radial set501.

In accordance with an embodiment, and as illustrated in FIG. 5A, theabrasive particles 522-526 can have substantially the same predeterminedrotational orientation relative to each other. For example, the abrasiveparticle 522 can have a longitudinal axis 531 that defines thepredetermined rotational orientation angle 532 relative to the radialaxis 512. Notably, the predetermined rotational orientation angle 532 ismeasured at the point where the longitudinal axis 531 is closest to theside surface 103. Moreover, the abrasive particle 523 can have alongitudinal axis 533 that defines a predetermined rotationalorientation angle 534 relative to the radial axis 514. The abrasiveparticle 524 can have a longitudinal axis 535 defining a predeterminedrotational orientation angle 536 relative to the radial axis 516. Theabrasive particle 525 can have a longitudinal axis 537 defining apredetermined rotational orientation angle 538 relative to the radialaxis 518. Furthermore, the abrasive particle 526 can have a longitudinalaxis 539 defining a predetermined rotational orientation angle 540relative to the radial axis 520. In accordance with an embodiment, eachof the predetermined rotational orientation angles 532, 534, 536, 538,and 540 can be the same. Still, in an alternative embodiment, theabrasive particles of a radial set, including for example abrasiveparticles 522-526 of the second radial set 521, may have a differentpredetermined rotational orientation angle with respect to each other.

In yet another embodiment, such as illustrated in FIG. 5A, the abrasiveparticles 502-506 of the first radial set 501 may be positioned closerto the side surface 103 and configured to conduct an initial materialremoval operation. The abrasive particles 522-526 of the second radialset 521 can be spaced at a greater distance from the side surface 103than the abrasive particles 502-506 of the first radial set 501. Assuch, the abrasive particles 522-526 can be positioned as backupabrasive elements configured to conduct material removal operationsafter some portion of the abrasive particles 502-506 of the first radialset 501 is worn.

The abrasive particles 522-526 of the second radial set 521 can havesubstantially the same axial position with respect to each other, suchthat the abrasive particles 522-526 are positioned within the sameradial plane 122. Furthermore, as will be appreciated, the abrasiveparticles 522-526 of the second radial set 521 can have at least oneabrasive characteristic that is substantially the same with respect toeach other. Suitable abrasive characteristics can include but are notlimited to, hardness, composition, average particle size, average grainsize, fracture toughness, two-dimensional shape, tip sharpness, typical,aspect ratio, and a combination thereof. Still, in at least onenon-limiting embodiment, the abrasive particles 522-526 of the secondradial set 521 can have at least one abrasive characteristic that isdistinct from each other. Moreover, it will be appreciated that theabrasive particles 502-506 of the first radial set 501 and the abrasiveparticles 522-526 and the second axial set 521 may have at least oneabrasive characteristic that can be substantially the same with regardto each other, including for example two-dimensional shape. Still, inanother alternative embodiment, the abrasive particles 502-506 of thefirst radial set 501 may have at least one abrasive characteristic thatis distinct from the abrasive particles 522-526 of the second radial set521.

As further illustrated in FIG. 5A, at least a portion of the abrasiveparticles of the first group 545 can have a particular cutting tip orcutting edge having a predetermined orientation relative to the sidesurface 103. For example, the abrasive particle 502 can have a cuttingtip 547 that has a particular orientation relative to the side surface103. Notably, the orientation of the cutting tip 547 may be defined bythe predetermined rotational orientation angle of the abrasive particle502.

In another embodiment, at least a portion of the abrasive particles inthe body may have a predetermined rotational orientation relative to anintended grinding direction 546 of the abrasive article. For example,the shaped abrasive particle 522 can have a cutting tip 548 having aparticular rotational orientation relative to the side surface 103,which in some embodiments includes the predetermined rotationalorientation angle 532. In certain instances, the predeterminedrotational orientation angle 532 can also define a rake angle relativeto the intended grinding direction 546 of the abrasive article 100. Inthe instance of the shaped abrasive particle 502, the rake angle has azero value because the shaped abrasive particle 502 has a predeterminedrotational orientation angle that orients the cutting tip 547substantially perpendicular to the intended grinding direction 546. Inthe instance of the shaped abrasive particle 522, the rake angle has apositive value because the shaped abrasive particle 522 has apredetermined rotational orientation angle 532 that inclines the cuttingtip 548 in the same direction as the intended grinding direction 546. Inanother embodiment, a shaped abrasive particle can include a rake anglewith a negative value, where a shaped abrasive particle has apredetermined rotational orientation angle that inclines a cutting tipin a direction opposite to the intended grinding direction 546. As such,it will be appreciated that the abrasive particles and the orientationof their cutting tips or cutting surfaces relative to the side surfacemay be controlled such that a suitable rake angle is created relative toan intended grinding direction 546 of the abrasive article 100, whichmay facilitate improved material removal performance.

Referring again to FIG. 1, in accordance with an embodiment, the body101 of the fixed abrasive article 100 can include multiple axial planes,including for example, the first axial plane 131 and the second axialplane 132. Furthermore, each axial plane may have one or more groups ofabrasive particles, including for example, the groups of abrasiveparticles 191 and 192. The groups of abrasive particles 191 and 192 canbe axial collections and/or axial sets in the respective axial planes131 and 132. Moreover, the abrasive particles of each group of abrasiveparticles 191 and 192 can have at least one abrasive characteristicand/or at least one orientation characteristic that is substantially thesame with respect to the other abrasive particles within the group,including (a) a predetermined rotational orientation angle, or arotational orientation in a plane defined by the length and the width ofthe particle; (b) a predetermined tilt angle, or a rotationalorientation in the plane defined by the length and the thickness of theparticle; and/or (c) a predetermined lateral axis rotational orientationangle, or a rotational orientation in the plane defined by the width andthe thickness of the particle. It should also be noted that certainparticles may utilize a combination of more than one type of rotationalorientation. In one embodiment, the abrasive particles of the group ofabrasive particles 191 can have at least one abrasive characteristicthat is substantially the same and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation,predetermined rotational orientation angle, predetermined tilt angle,and/or predetermined lateral rotational orientation angle) that issubstantially the same with respect to the other abrasive particleswithin the group 191. Still, in another embodiment, at least oneabrasive particle within the group of abrasive particles 191 can have atleast one abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation,predetermined rotational orientation angle, predetermined tilt angle,and/or predetermined lateral rotational orientation angle) that isdifferent compared to at least one other abrasive particle within thegroup of abrasive particles 191. For yet another embodiment, at leastone abrasive particle within the group of abrasive particles 191 canhave at least one abrasive characteristic and/or at least oneorientation characteristic (e.g., predetermined rotational orientation,predetermined rotational orientation angle, predetermined tilt angle,and/or predetermined lateral rotational orientation angle) that isdifferent compared to at least one other abrasive particle within thegroup of abrasive particles 192 associated with the axial plane 132.

As further illustrated in FIG. 1, the body 101 of the fixed abrasivearticle 100 can include multiple radial planes, including for example,the first radial plane 121 and the second radial plane 122. Furthermore,each radial plane may have one or more groups of abrasive particles,such as the groups of abrasive particles 105 and 106, which can be inthe form of radial groups and/or radial sets of abrasive particles. Inat least one embodiment, the abrasive particles of each group ofabrasive particles 105 and 106 can have at least one abrasivecharacteristic and/or at least one orientation characteristic (e.g.,predetermined rotational orientation and/or predetermined lateralrotational orientation) that is substantially the same with respect tothe other abrasive particles of the groups of abrasive particles 105 and106. In one embodiment, the abrasive particles of the group of abrasiveparticles 105 can have at least one abrasive characteristic and/or atleast one orientation characteristic (e.g., predetermined rotationalorientation and/or predetermined lateral rotational orientation) that issubstantially the same with respect to the other abrasive particleswithin the group 105. Still, in another embodiment, at least oneabrasive particle within the group of abrasive particles 105 can have atleast one abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation and/orpredetermined lateral rotational orientation) that is different comparedto at least one other abrasive particle within the group of abrasiveparticles 105. For yet another embodiment, at least one abrasiveparticle within the group of abrasive particles 105 can have at leastone abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation and/orpredetermined lateral rotational orientation) that is different comparedto at least one other abrasive particle within the group of abrasiveparticles 106 associated with the radial plane 121.

In accordance with an embodiment, the body 101 can include a first groupof abrasive particles 106 in the first radial plane 121 and a secondgroup of abrasive particles 105 within a second radial plane 122. Asillustrated, the first group of abrasive particles 106 in the firstradial plane 121 can be spaced apart axially from the second group ofabrasive particles 105 in the second radial plane 122. The second groupof abrasive particles 105 within the radial plane 122 can have any ofthe attributes of the abrasive particles described herein, including forexample, the first group of abrasive particles 545. For example, thesecond group of abrasive particles 105 can include shaped abrasiveparticles or elongated abrasive particles. In another embodiment, thesecond group of abrasive particles 105 can be arranged in a controlleddistribution relative to each other. As will be appreciated, the secondgroup of abrasive particles 105 in the second radial plane 122 can havea predetermined position within the radial plane 122 and havesubstantially the same axial position within the radial plane 122 withrespect to each other. Still, in other embodiments, the abrasiveparticles in the second group 105 can have a different radial positionwith respect to each other within the radial plane 122. In at least oneembodiment, the second group of abrasive particles 105 within the secondradial plane 122 can have a predetermined rotational orientationrelative to the side surface 103 of the body 101. Moreover, the firstgroup of abrasive particles 106 can have a first predeterminedrotational orientation and the second group of abrasive particles 105can have a second predetermined rotational orientation that may bedifferent than the predetermined rotational orientation of the firstgroup of abrasive particles 106.

The abrasive particles of the second group 105 can have at least oneabrasive characteristic that is the same with respect to each other,including for example abrasive characteristics such as hardness,composition, average particle size, average grain size, fracturetoughness, two-dimensional shape, tip sharpness, tip angle, aspectratio, and a combination thereof. Moreover, the abrasive particles ofthe second group 105 can have at least one abrasive characteristic thatis substantially the same as the abrasive particles of the first group106. Still, in another embodiment, the abrasive particles of the secondgroup 105 can have at least one abrasive characteristic that is distinctfrom the abrasive characteristic of the abrasive particles of the firstgroup 106.

The body 101 of the fixed abrasive 100 can include a plurality of groupsof abrasive particles, including the first group of abrasive particles106 in the radial plane 121 and second group of abrasive particles 105in the radial plane 122. Moreover, each of the groups of abrasiveparticles can include a plurality of radial sets of abrasive particleswherein each of the radial sets is spaced at different radial distancesfrom the center of the body and the side surface 103 relative to eachother. For example, the first group of abrasive particles 106 caninclude a plurality of radial sets and the second group of abrasiveparticles 105 can include a plurality of radial sets. In certainembodiments, the radial sets may establish concentric rings of abrasiveparticles around the central opening 185. However, it will beappreciated that a radial set may extend for a portion of an entirecircumference of the body 101. In at least one instance, a radial setmay extend for an entire circumference of the body at a given radialdistance from the center of the body 101.

FIG. 6 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles as viewed from a side surface in accordancewith an embodiment. As illustrated, and as referenced in FIG. 5A, thebody 101 can include abrasive particles 502, 503, 504, 505, and 506(502-506) as part of the first group 501. The body can include thereinforcing member 141. Furthermore, the body can include a second groupof abrasive particles 630 including abrasive particles 631, 632, 633,634, 635, 636, and 637 (631-637). In accordance with an embodiment, atleast a portion of the abrasive particles in the body 101, includingshaped abrasive particles and/or elongated abrasive particles, can havea predetermined rotational orientation including a predetermined lateralaxis rotational orientation angle. For example, the abrasive particle502 can have a lateral axis 671 that defines a width of the abrasiveparticle 502. The lateral axis 671, along with a normal axis 602 thatextends from the particle 502 (as viewed from the side surface 103) andis normal to one of the major surfaces of the body 101 (e.g., the uppersurface 102) further define a predetermined lateral axis rotationorientation angle 601. A portion of abrasive particles in the body 101may have a predetermined lateral axis rotational orientation angle tofacilitate improved material removal operations. In accordance with anembodiment, the group of abrasive particles 501 including abrasiveparticles 502-506 can be placed within the body 101 such that each ofthe abrasive particles 502-506 can have substantially the samepredetermined lateral axis rotational orientation angle. For example,the abrasive particle 503 can have a lateral axis 672 that, along with anormal axis 604, define a predetermined lateral axis rotationalorientation angle 603. Additionally, the abrasive particle 504 can havea lateral axis 673 that is used to define a predetermined lateral axisrotational orientation angle 605 relative to a normal axis 606. Theabrasive particle 505 can have a lateral axis 674 defining apredetermined lateral axis rotational orientation angle 607 relative toa normal axis 608. Moreover, the abrasive particle 506 can have alateral axis 675 defining a predetermined lateral axis rotationalorientation angle 609 relative to a normal axis 610. In accordance withan embodiment, each of the predetermined lateral axis rotationalorientation angles 601, 603, 605, 607, and 609 of the abrasive particles502-506 can have substantially the same value. Still, in at least oneembodiment, one or more of the abrasive particles 502-506 of the firstgroup 501 can have a predetermined lateral axis rotational orientationangle 601, 603, 605, 607, 609 that can be distinct from each other.

In accordance with an embodiment, the fixed abrasive article can beformed such that at least a portion of the abrasive particles in thebody, including shaped abrasive particles and/or elongated abrasiveparticles, can be placed within the body to have a predetermined lateralaxis rotational orientation angle of not greater than 90°, such as notgreater than 80°, not greater than 70°, not greater than 60°, notgreater than 50°, not greater than 40°, not greater than 30°, notgreater than 20°, not greater than 10°, or even not greater than 5°.Still, in another embodiment, the average predetermined lateral axisrotational orientation angle for the portion of abrasive particles canbe at least 0.1°, such as at least 1°, at least 3°, at least 5°, atleast 10°, at least 20°, at least 30°, at least 40°, or even at least50°. It will be appreciated that the portion of the abrasive particlescan have a predetermined lateral axis rotational orientation anglewithin a range including any of the minimum and maximum values notedabove. Moreover, reference to the predetermined lateral axis rotationalorientation angle for a portion of abrasive particles can includereference to an average value of the predetermined lateral axisrotational orientation angle.

In accordance with another embodiment, at least a portion of theabrasive particles within the body 101, including shaped abrasiveparticles and/or elongated abrasive particles, can have a particularstandard deviation of the predetermined lateral axis rotationalorientation angle that may facilitate improved performance. For example,the portion of abrasive particles can have a standard deviation of thepredetermined lateral axis rotational orientation angle of not greaterthan 20 degrees, such as not greater than 18 degrees, not greater than16 degrees, not greater than 14 degrees, not greater than 12 degrees,not greater than 10 degrees, not greater than 9 degrees, not greaterthan 8 degrees, not greater than 7 degrees, or even not greater than 6degrees. Still, in at least one non-limiting embodiment, a portion ofthe abrasive particles can have a standard deviation of thepredetermined lateral axis rotational orientation angle of at least 0.1degrees, such as at least 0.5 degrees, or even at least 1 degree. Itwill be appreciated that the standard deviation of the predeterminedlateral axis rotational orientation angle can be with a range includingany of the minimum and maximum values noted above.

As further illustrated in FIG. 6, each of the abrasive particles 631-637of the second group 630 can have a particular predetermined lateral axisrotational orientation angle with respect to the bottom surface 104 ofthe body. For example, the abrasive particle 631 can have a lateral axis681 that defines a width of the abrasive particle 631. The lateral axis681, along with a normal axis 661 that extends from the particle 631 (asviewed from the side surface 103) and is normal to one of the majorsurfaces (e.g., the bottom surface 104) of the body 101, define apredetermined lateral axis rotational orientation angle 641. Theabrasive particle 632 can have a lateral axis 682 defining apredetermined lateral axis rotational orientation angle 642 relative tothe normal axis 662. Additionally, the abrasive particle 633 can have alateral axis 683 defining a predetermined lateral axis rotationorientation angle 643 relative to the normal axis 663. The abrasiveparticle 634 can have a lateral axis 684 defining a predeterminedlateral axis rotational orientation angle 644 relative to the normalaxis 664. The abrasive particle 635 can have a lateral axis 685 defininga predetermined lateral axis rotational orientation angle 645 relativeto the normal axis 665. The abrasive particle 636 can have a lateralaxis 686 defining a predetermined lateral axis rotational orientationangle 646 relative to the normal axis 666. Finally, the abrasiveparticle 637 can have a lateral axis 687 defining a predeterminedlateral axis rotational orientation angle 647 relative to the normalaxis 667. It will be appreciated that each of the abrasive particles631-637 can have the same attributes as the abrasive particles 502-506of the first group 501.

According to another aspect, the body 101 can include groups of abrasiveparticles, including shaped abrasive particles and/or elongated abrasiveparticles, contained within axial planes (i.e., axial collections ofabrasive particles), including for example axial planes 131 and 132.Moreover, there may be groups of abrasive particles contained withinsectors, including for example sector 184 extending between axial planes131 and 132. In one embodiment, the body 101 can include a plurality ofaxial collections of abrasive particles, wherein each axial collectionincludes a plurality of abrasive particles contained within an axialplane within the body. For example, the axial plane 131 can include theaxial collection of abrasive particles 191. Furthermore, the axial plane132 can include the axial collection of abrasive particles 192.

FIG. 7 includes a cross-sectional view of a portion of a body of a fixedabrasive article in accordance with an embodiment. A first axialcollection of abrasive particles 701 can include abrasive particles 702,703, 704, 705, 706, and 707 (702-707) within a first axial plane 131 ofthe body 101. The abrasive particles 702-707 can include shaped abrasiveparticles and/or elongated shaped abrasive particles. In accordance withan embodiment, each of the abrasive particles 702-707 of the first axialcollection 701 are in a predetermined position and are substantiallylying flat with respect to the major surfaces 102 and 104, such that thelongitudinal axes 721, 722, 723, 724, 725, and 726 of each of theabrasive particle 702-707 are extending substantially perpendicular tothe side surface 103 of the body 101 and substantially parallel to themajor surfaces 102 and 104 of the body 101. It will be appreciated thatthe axial collection of abrasive particles 701 can include any of thefeatures described in accordance with other groups of abrasive particlesof the environment here including, for example, groups of abrasiveparticles in a radial set and or a first group abrasive particles in aradial plane.

In accordance with an embodiment, each of the abrasive particles 702-707of the first axial collection 701 can have a predetermined rotationalorientation relative to the side surface 103 of the body 101. Thepredetermined rotational orientation can be defined by a predeterminedrotational orientation angle as defined in other embodiments herein. Theabrasive particles 702-707 can have the same positive, zero, or negativevalues of predetermined rotational orientation angle as described inother embodiments herein. Moreover, it will be appreciated that each ofthe abrasive particles 702-707 of the first axial collection 701 canhave substantially the same predetermined rotational orientationrelative to each other. Still, in other instances, the predeterminedrotational orientation of at least two of the abrasive particles 702-707of the first axial collection may be different with respect to eachother.

According to one embodiment, the abrasive particles 702-707 of the firstaxial collection 701 can be arranged in a controlled distributionrelative to each other. That is, the abrasive particles 702-707 can bespaced at a particular distance relative to each other that can define aparticular distribution, such as a pattern.

In accordance with another embodiment, the abrasive particles 702-707 ofthe first axial collection 701 can have at least one abrasivecharacteristic that is substantially the same including, but not limitedto, hardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof. Still, it will be appreciatedthat, in certain instances, at least two of the abrasive particles702-707 of the first axial collection 701 may have at least one abrasivecharacteristic that is different as compared to each other.

As further illustrated in FIG. 7, the group of abrasive particles withinthe axial plane 131 can include a second axial collection 710 ofabrasive particles 711, 712, 713, 714, 715, (711-715). The abrasiveparticles 711-715 can include shaped abrasive particles and/or elongatedshaped abrasive particles. In accordance with an embodiment, each of theabrasive particles 711-715 of the second axial collection 710 can have apredetermined position and can be substantially lying flat with respectto the major surfaces 102 and 104 like the abrasive particles 702-707.

The abrasive particles 711-715 can have any of the attributes of theabrasive particles 702-707 of the first axial collection 701. Forexample, each of the abrasive particles 711-715 of the second axialcollection 710 can have substantially the same predetermined rotationalorientation with respect to each other and with respect to the sidesurface 103 of the body 101. In addition, the abrasive particles 711-715of the second axial collection 710 can be arranged in a controlleddistribution relative to each other or relative to the abrasiveparticles 702-707 of the first axial collection 701. For example, thecontrolled distribution can include an ordered distribution of theabrasive particles 711-715 of the second axial collection 710 relativeto each other. In one embodiment, the abrasive particles 711-715 of thesecond axial collection 710 can have a different axial position, radialposition, and/or predetermined rotational orientation compared to theabrasive particles 702-707 of the first axial collection 701. In anotherembodiment, the group of abrasive particles within the axial plane 131can be in a controlled, non-shadowing arrangement. For example, two ormore particles within the axial plane 131 (e.g., particles 702, 711,703, and 712) can be intentionally staggered relative to one another,such that each of the particles occupies a position in a differentradial plane. It has been noted that it may be particularly advantageousto stagger the particles relative to each other, such that particles inthe same axial plane (e.g. the group of abrasive particles within theaxial plane 131) can occupy different axial and radial positionsrelative to each other. Moreover, it is contemplated that abrasiveparticles within the same axial plane may be spaced at differentdistances relative to the side surface 103, such that during use andwear of the abrasive article, new and fresh cutting tips arecontinuously exposed to facilitate suitable grinding operations.Moreover, it will be appreciated that position and rotationalorientation of abrasive particles within different groups (e.g.,different radial groups) may be controlled relative to each other.

It will be appreciated that the abrasive particles 711-715 of the axialcollection 710 can have at least one abrasive characteristic that issubstantially the same relative to each other. Suitable examples ofabrasive characteristics include hardness, composition, average particlesize, average grain size, fracture toughness, two-dimensional shape, tipsharpness, tip angle, aspect ratio, and a combination thereof. Moreover,it will be appreciated that various different abrasive particles ofdifferent axial collections may have substantially the same abrasivecharacteristic relative to each other. However, in an alternativeembodiment, different abrasive particles of different axial collectionscan have at least one abrasive characteristic that is different withrespect to each other. For example, the abrasive particles 702-707 ofthe axial collection 701 can have at least one abrasive characteristicthat is different than the abrasive particles 711-715 of the axialcollection 710.

It will be appreciated that different axial planes can include differentaxial collections of abrasive particles. For example, the axial plane131 can include a first axial collection including for example abrasiveparticles 702-707 of the first axial collection 701 and the axial plane132 can include a second collection, including for example, the secondaxial collection 710 of abrasive particles 711-715. The abrasiveparticles of an axial collection can have substantially the same angularposition within the body with respect to each other. Moreover, incertain instances, the abrasive particles of an axial collection canhave substantially the same radial position within the body with respectto each other. For example, the abrasive particles 711-715 of the secondaxial collection 710 can have substantially the same radial positionwith respect to each other. As further illustrated, the abrasiveparticles 711-715 of the second axial collection 710 can have adifferent axial position relative to each other, such that the abrasiveparticle 711 may be closer to the upper surface 102 relative to theabrasive particle 715. Still, in certain instances, the abrasiveparticles of any of the axial collections including, for example,abrasive particles 711-715 may be formed to have a different radialposition with respect to each other. For example, in certain instancesthe abrasive particle 702-707 and abrasive particle 711-715 may be partof the same axial collection. In certain in such instances, the abrasiveparticle 702 can have a different radial position relative to theabrasive particle 711. That is, the abrasive particle 702 can bepositioned at a different radial distance from the center of the body101 and closer to the side surface 103 relative to the position of theabrasive particle 711.

FIG. 8 includes an illustration of a portion of a fixed abrasivearticle, as viewed in a cross-sectional plane that is parallel to anaxial plane of the article, in accordance with an embodiment. The body101 (FIG. 1) can include abrasive particles 801, 802, 803, 804, and 805(801-805), which may be coupled to each other by an orientationstructure 806. As illustrated, the abrasive particle 805 can intersectthe side surface 103 of the body 101 and may be at least partiallyprotruding from the volume of the body 101 and extending radially beyondthe side surface 103. In accordance with an embodiment, the orientationstructure 806 can define a structure coupling at least a portion of theabrasive particles to each other within the body 101. In certaininstances, the orientation structure 806 can be coupled to a majority ofthe abrasive particles, which may include shaped abrasive particlesand/or elongated abrasive particles.

In at least one embodiment, the orientation structure 806 can be aseparate phase from the bond material 825. In accordance with anembodiment, at least a portion of the abrasive particles, including forexample, abrasive particles 801-805 may be coupled to the orientationstructure 806 that extends throughout a portion of the bond material 825within the body 101. In certain instances, the orientation structure 806can have a different composition compared to the bond material 825.Notably, the orientation structure 806 can be a material that defines aseparate phase from the bond material 825. In accordance with anembodiment, the orientation structure 806 can include a material such asa metal, ceramic, glass, an organic material, a polymer, and acombination thereof.

In certain instances, the orientation structure 806 may extendthroughout the entire volume of the body 101. In other instances, theorientation structure 806 may extend for at least a majority of thetotal volume of the body 801. In still another embodiment, theorientation structure 806 may extend throughout at least a portion ofthe body 801, which may be greater or less than a majority of the entirevolume of the body 101. In particular instances, the orientationstructure 806 can be coupled to the abrasive particles and configured tocontrol three-axis position, including for example, the predeterminedposition and/or predetermined rotational orientation of the abrasiveparticles within the body 101. For example, the orientation structure806 can be coupled to the abrasive particles 801-805 and configured tocontrol the predetermined position and predetermined rotationalorientation, including the predetermined rotational orientation angle,of the abrasive particles 801-805 relative to the side surface 103.

In accordance with an embodiment, the orientation structure 806 may havea particular hardness relative to the hardness of the bond material 825,which may facilitate certain material removal operations. For example,the orientation structure 806 can have a hardness that is less than ahardness of the bond material 825. Still, in accordance with anotherembodiment, the orientation structure 806 can have a hardness that isgreater than a hardness of the bond material 825. In yet anotherembodiment, the orientation structure 806 can have a hardness that issubstantially the same as a hardness of the bond material 825. As usedherein, substantially the same is reference to two values that arewithin 5% of each other based on the larger value.

In another embodiment, the orientation structure 806 may have aparticular hardness with respect to the abrasive particles, includingabrasive particles 801-805. For example, in at least one embodiment, theorientation structure 806 can have a hardness is less than a hardness ofthe abrasive particles 801-805. The relative hardness of the orientationstructure 806 to the abrasive particles 801-805 may be suited tofacilitate improved grinding performance. Still, in certain instances,the orientation structure 806 can have a hardness that is substantiallythe same as the hardness of the abrasive particles.

The orientation structure 806 can be coupled to the abrasive particlesand configured to control the predetermined position of the abrasiveparticles within the volume of the body 101 including a radial position,an axial position, and an angular position of the abrasive particles inthe body 101. In another embodiment, the orientation structure 806 canbe coupled to each of the abrasive particles including shaped abrasiveparticles and/or elongated abrasive particles throughout the body 101.

In accordance with another embodiment, the orientation structure 821 canbe coupled to various groups of abrasive particles including a firstgroup of abrasive particles 810, 811, 812, 813, 814, and 815 (810-815)and a second group of abrasive particles 816, 817, 818, 819, and 820(816-820). As illustrated, the first group of abrasive particles 810-815can include abrasive particles positioned in a first radial plane andthe second group of abrasive particle 816-820 can include abrasiveparticles positioned in a second radial plane. As illustrated herein,the orientation structure 821 can extend between groups of abrasiveparticles including abrasive particles 810-815 and 816-820 and bind themto each other. In accordance with an embodiment, the orientationstructure 821 can have various shapes and constructions, including forexample, a web, woven material, a nonwoven material, paper, fabric, aspun woven material, a film, a laminate, a composite, and a preformhaving regions sized and shaped to contain one or more abrasiveparticles, including a shaped abrasive particle and/or elongatedabrasive particle.

In another embodiment, the body 101 may include a first orientationstructure, such as orientation structure 806 coupled to a first group ofabrasive particles 801-805, and a second orientation structure, such asorientation structure 821, different than the first orientationstructure 806 and coupled to the second group of abrasive particles810-820. In accordance with an embodiment, the first orientationstructure 806 can be coupled to the first group of abrasive particles801-805 positioned in a first radial plane within the body 101 and thesecond orientation structure 821 can be coupled to a second group ofabrasive particles 810-820 positioned in a second radial plane withinthe body 101. More particularly, it will be appreciated that the firstorientation structure may be coupled to a first radial set of abrasiveparticles within a radial plane and the second orientation structure canbe coupled to a second radial set of abrasive particles within a secondradial plane of the body. It will be appreciated that the first andsecond radial planes can be distinct from each other as describedherein.

In an alternative embodiment, various orientation structures may be usedand coupled to abrasive particles of different portions of abrasiveparticles within the body including, for example, different axialcollections of abrasive particles and/or different axial sets ofabrasive particles. For example, in an embodiment, a first orientationstructure may be coupled to a group of abrasive particles in a firstaxial plane associated with a first axial collection and a secondorientation structure can be coupled to a second axial collection ofabrasive particles within a second axial plane. Still, a single axialplane may utilize a plurality of orientation structures to couple one ormore axial collections of abrasive particles therein.

In a further embodiment, the abrasive particles within the axial planedepicted in FIG. 8, namely particles 801-805, 811-815, and 816-820, canbe arranged in a controlled distribution relative to each other. Forexample, the controlled distribution can include (a) an ordereddistribution of the abrasive particles 801-805 relative to each other;(b) an ordered distribution of the abrasive particles 811-815 relativeto each other; and/or (c) an ordered distribution of the abrasiveparticles 816-820 relative to each other. In another embodiment, theabrasive particles 801-805, 811-815, and 816-820 within the axial planecan be in a controlled, non-shadowing arrangement. For example, each ofthe depicted particles in FIG. 8 can be intentionally staggered relativeto one another, such that each of the particles within the axial planeoccupies a different radial position (e.g., a different distance fromthe center of the body 101). That is, when the particles are viewed topdown in the body 101 (e.g., viewed from a plane parallel to the majorsurfaces 102 or 104), the particles in one radial plane of the body 101(e.g., the particles 801-805) do not directly overlie the particles inanother radial plane of the body 101 (e.g., either the particles 811-815or the particles 816-820). Furthermore, the particles in one radialplane of the body 101 also may have different rotational orientations(e.g., different predetermined rotational orientation angles, differentpredetermined tilt angles, different predetermined lateral axisrotational orientation angles, and/or different rake angles) relative toone another or relative to the particles in another radial plane of thebody 101.

FIG. 9 includes a flowchart providing a method of forming a fixedabrasive article according to an embodiment. As illustrated, the processmay be initiated at step 901 by forming a mixture including a precursorbond material. The precursor bond material can include material such asa ceramic, glass, frit, an organic material, a polymer, a resin, ametal, and a combination thereof. In certain instances, the precursorbond material may include a powder material. Still in another instance,the precursor bond material may include a liquid material. It will beappreciated that the precursor bond material may include a combinationof phases, including both solid and liquid materials, which can beprocessed later to form the finally-formed bond material of the fixedabrasive article.

As further illustrated in FIG. 9, the process can continue at step 902by providing a forming structure configured to position abrasiveparticles in a predetermined position within the precursor bondmaterial. More particularly, FIGS. 10A-10C include illustrations of asystem for forming a fixed abrasive article according to an embodiment.FIG. 10A includes a system 1001 including a production tool 1002 inwhich the green body of the fixed abrasive article can be formed andprocessed to form the finally-formed fixed abrasive article. Inaccordance with one embodiment, the system 1001 includes a formingstructure 1006 having at least one opening 1008, in which the abrasiveparticles, such as shaped abrasive particles and/or elongated abrasiveparticles, are configured to pass through for deposition onto theprecursor bond material 1003 in a predetermined position and/orpredetermined rotational orientation. In at least one embodiment asillustrated in FIG. 10A, the abrasive particles 1007 can be deposited ina predetermined position on the precursor bond material 1003, such asthe abrasive particles 1004. As further illustrated, the formingstructure 1006 can include a container (e.g., a hopper) configured tocontain a plurality of abrasive particles 1007 and deposit them througha channel region 1009 ending in the opening 1008. The abrasive particlesmay be fed though the forming structure by gravity, vibration, or by theapplication of another force. It will be appreciated that control of thedeposition process of the abrasive particles 1004 on the precursor bondmaterial 1003 can facilitate formation of a fixed abrasive article wherethe abrasive particles have a predetermined position and/orpredetermined rotational orientation.

Furthermore, the forming structure 1006 can be moved in the directions1005 and 1010 to facilitate controlled placement and orientation of theabrasive particles 1004 on the precursor bond material 1003. Inaccordance with another embodiment, the abrasive particles 1007 areconfigured to pass through the at least one opening 1008 for depositionon or within the precursor bond material 1003 with a predeterminedrotational orientation relative to a side surface of the body of thefixed abrasive article, which can be defined by a side surface 1031 ofthe production tool 1002. The forming structure 1006 can be configuredto move and control the predetermined position of a single abrasiveparticle by controlling the position of the forming structure 1006relative to the precursor bond material 1003. That is, the formingstructure 1006 can move in directions 1005 and 1010 and place individualabrasive particles 1004 on the precursor bond material 1003 thuscontrolling the predetermined position and/or predetermined rotationalorientation of the abrasive particles 1004 on the precursor bondmaterial 1003, and thus control the predetermined position and/orpredetermined rotational orientation of the abrasive particles 1004 inthe finally-formed abrasive article.

As further illustrated, FIG. 10B includes a second step in the formingprocess, which can include the deposition of a second layer of precursorbond material 1020 over the abrasive particles 1004. After deposition ofthe second layer of precursor bond material 1020, the process maycontinue by further deposition of abrasive particles 1007 from theforming structure 1006 on the second layer of precursor bond material1020, as illustrated in FIG. 10C. In at least one embodiment, the secondlayer of abrasive particles 1030 may be deposited in the same manner asthe abrasive particles 1004, such that they are placed on the secondlayer of precursor bond material 1020 with a predetermined positionand/or predetermined rotational orientation, which facilitates theformation of a fixed abrasive article wherein the second layer ofabrasive particles 1030 have a predetermined position and/orpredetermined rotational orientation. The abrasive particles 1004 and1030 can include shaped abrasive particles and/or elongated abrasiveparticles.

In particular instances, the process of forming the fixed abrasivearticle can include placing a first group of abrasive particles in afirst radial plane within the precursor bond material, such asillustrated in FIG. 10A, wherein the abrasive particles 1004 are placedon or overlying a first layer of precursor bond material 1003. Theprocess can further include depositing a precursor bond material overthe first group of abrasive particles 1004 in the first radial plane,such as illustrated in FIG. 10B. As will be appreciated and as furtherillustrated in FIG. 10C, the process can further include depositing asecond group of abrasive particles 1030 that may be associated with asecond radial plane overlying the first group of abrasive particles 1004the first radial plane. While reference has been made herein to thedeposition of abrasive particles in layers, such as radial planes, itwill be appreciated that the abrasive particles may be deposited ingroups, which can be associated with a group in a radial plane, a radialset, an axial collection, a portion of an axial collection, a sector,and a combination thereof.

It will be appreciated that one or more reinforcing members may also beprovided at any point within the forming process, such as before orafter the deposition of any of the precursor bond material layers andbefore or after the deposition of any of the abrasive particles.Moreover, the forming process may include one or more processing stepsbetween the deposition of any one of the components (e.g., abrasiveparticles, layer of precursor bond material, reinforcing member,additives, etc.) used to form the fixed abrasive article. Such processescan include treatment or partial treatment of the bond material. Forexample, in at least one embodiment, the precursor bond material 1003can be cured or partially cured before the deposition of furthercomponents used to form the fixed abrasive article. Moreover, it will beappreciated that while certain abrasive particles may be deposited usingthe forming structure, further processing may be utilized for depositionof one or more other components, including for example, otherparticulate matter (e.g., diluent grains, fillers, pore formers, etc.).Deposition of the one or more other components can be conducted usingthe forming structure 1006 or a separate forming structure to controlthe predetermined position and/or predetermined rotational orientationof the one or more other components (e.g., diluent grains, fillers, poreformers, etc.). Still, in certain other instances, the process ofdeposition of the one or more other components can include deposition ofthe materials in a generally random manner.

It will be further appreciated that controlling one or more processingvariables can facilitate the formation of a fixed abrasive article wherethe abrasive particles have a predetermined position and/orpredetermined rotational orientation. For example, certain processingvariables related to the bond and the abrasive particles being used,including the composition of the precursor bond material and the averagesize of the abrasive particles, can impact the final predeterminedposition and/or predetermined rotational orientation of the abrasiveparticles within the fixed article. Certain processing conditionsrelated to curing of the green body can also contribute to the finalpositioning of the abrasive particles. For example, without wishing tobe bound by a particular theory, it is believed that by controllingcertain curing conditions (e.g., curing pressures, temperatures, andother conditions that prevent the precursor bond material from curingbefore the placement of the particles within the precursor bond materialis completed), the placement of the abrasive particles in theirpredetermined positions and/or predetermined rotational orientationsalso can be better controlled.

FIG. 11 includes a system for forming a fixed abrasive article accordingto an embodiment. As illustrated, the system 1100 can include aproduction tool 1102 having a first layer of precursor bond material1103 formed therein. Additionally, a group of abrasive particles 1104have been deposited on the first layer of precursor bond material 1103.Notably, the abrasive particles 1104 which are deposited can be selectedfrom a group of abrasive particles 1112 contained in a hopper 1111.During processing, a forming structure 1106 can select a single abrasiveparticle from the group 1112 at position 1110 and move from the position1110 to a position near the precursor bond material 1103 for depositionof an abrasive particle on or within the precursor bond material 1103 ina predetermined position and/or a predetermined rotational orientation.In accordance with an embodiment, the forming structure 1106 may be anoptical pick-and-place machine capable of rapidly selecting andcontrolling the predetermined position and/or predetermined rotationalorientation of a single abrasive particle at a time. For example, asillustrated, the forming structure 1106 can be moved from position 1110along the path 1109 with a single abrasive particle of the group ofabrasive particles 1112, and may further have complete three-spacemovement capabilities including, but not limited to, movement in avertical direction 1108 and horizontal direction 1105. The formingstructure 1106 can have at least one control head 1107 configured tohold and deposit a single abrasive particle. It will be appreciated thatthe process may employ a forming structure having a plurality of controlheads, each of which are configured to facilitate controlled depositionof an individual grain on or within the precursor bond material 1103with a predetermined position and/or a predetermined rotationalorientation.

In accordance with another embodiment, a forming structure utilized tofacilitate controlled deposition of one or more abrasive particles witha predetermined position and/or predetermined rotational orientation canhave a plurality of openings. FIG. 12A includes an illustration of asystem for forming a fixed abrasive article according to an embodiment.The system 1200 includes a production tool 1202 and a forming structure1205 that can have a plurality of openings 1206 configured to allow thepassage of the abrasive particles 1204 through the openings 1206 in theforming structure 1205 for deposition of the abrasive particles 1204 onor within the precursor bond material 1203 with a predetermined positionand/or predetermined rotational orientation relative to a side surface1030 of the production tool and, ultimately, a side surface of thefinally-formed fixed abrasive article. Utilizing a forming structure1205 with a plurality of openings 1206 can facilitate rapid andsimultaneous placement of a plurality of abrasive particles 1204, suchas shaped abrasive particles and/or elongated abrasive particles, on orwithin the precursor bond material 1203 with a predetermined positionand/or predetermined rotational orientation.

Turning briefly to FIG. 21B and in accordance with an embodiment, aforming structure 2100 is depicted from a top-down perspective. Theforming structure 2100 includes a plurality of portions, such asportions 2150, positioned within the production tool 2100. The portions2150 can be permanently affixed in any suitable configuration to theforming structure 2100 or, alternatively, can be adjusted by anysuitable means to create any suitable configuration within the formingstructure 2100. As shown in FIG. 21B, the plurality of portions 2150 arepositioned so as to be parallel with a plurality of radial axesradiating from the center of the forming structure 2100.

The plurality of portions 2150 can be positioned not only to be parallelwith radial axes radiating from the center of the forming structure2100, but each portion 2150 also is spaced apart from adjacent portions2150. In an embodiment, the average width (W) of an opening betweenadjacent portions 2150 can be selected to facilitate placement ofabrasive particles in predetermined positions and/or predeterminedrotational orientations within the final fixed abrasive article. Forexample, the average width W of the openings between adjacent portions2150 can be adjusted to correspond to a physical dimension of theabrasive particles (e.g., their average length, width, or thickness).

In an embodiment, the average width W can be controlled relative to alargest dimension of an abrasive particle (i.e., the average width Wbetween adjacent portions 2150 can correspond to a largest dimension ofa shaped abrasive particle or elongated abrasive particle). For example,the portions 2150 can be placed such that there is an average width Wbetween adjacent portions 2150, where the average width W correspondsto, for example, an average length of the shaped and/or elongatedabrasive particles. In an embodiment, the width of the opening betweenadjacent portions 2150 can vary from a central axis or inner diameter ofthe forming structure 2100 to a side surface or outer diameter of theforming structure 2100. More particularly, the width of the openingbetween adjacent portions 2150 can increase from a width at the innerdiameter of the forming structure 2100 to a greater width at the outerdiameter of the forming structure 2100. In one example, the width of theopening between adjacent portions 2150 can be approximately 4millimeters at the inner diameter of the forming structure 2100. Thewidth of the opening between adjacent portions 2150 can vary betweenapproximately 5.23 millimeters (for one configuration of the portions2150 within the forming structure 2100) and 6.17 millimeters (foranother configuration of the portions 2150 within the forming structure2100) at the outer diameter of the forming structure. Thus, the averagewidth W between adjacent portions could be approximately 4.615millimeters in one embodiment (i.e., for one configuration of theportions 2150 within the forming structure 2100) or the average width Wcould be approximately 5.085 millimeters in another embodiment (i.e.,for another configuration of the portions 2150 within the formingstructure 2100).

Then the mixture including the abrasive particles can be deposited intothe forming structure 2100. The portions 2150 can facilitate not onlythe positioning of the abrasive particles (i.e., by positioning theabrasive particles between the portions 2150), but also can facilitatethe orientation of the abrasive particles, by positioning the abrasiveparticles in a lying flat configuration, such that the longest dimensionof the abrasive particles is substantially parallel to a major surfaceof the forming structure 2100 and, ultimately, a major surface of thefinal fixed abrasive article. In such a configuration, the abrasiveparticles can be positioned between the portions 2150 with a majorsurface of the abrasive particle lying parallel to a major surface ofthe final fixed abrasive article. In an embodiment, the average width Wof the openings between adjacent portions 2150 can be not greater thanthe average length of the abrasive particles, such as not greater than95%, not greater than 90%, not greater than 85%, not greater than 80%,not greater than 75%, or even not greater than 50% of the average lengthof the abrasive particles. In another embodiment, the average width Wbetween adjacent portions 2150 can be not greater than the averagethickness of the abrasive particles, such as not greater than 95%, notgreater than 90%, not greater than 85%, not greater than 80%, notgreater than 75%, or even not greater than 50% of the average thicknessof the abrasive particles. In another embodiment, the average width Wbetween adjacent portions 2150 can be not greater than the average widthof the abrasive particles, such as not greater than 95%, not greaterthan 90%, not greater than 85%, not greater than 80%, not greater than75%, or even not greater than 50% of the average width of the abrasiveparticles.

Turning briefly to FIG. 21C, a portion of the forming structure 2100 isillustrated from a top-down perspective with another configuration ofthe portions 2150. The portions 2150 can be positioned at any suitableangle relative to a radial axis of the forming structure 2100. Forexample, in FIG. 21C, the portions 2150 are positioned at a 45° angle toa radial axis of the forming structure 2100. As discussed above, theopenings between adjacent portions 2150 can include an average width W.That average width W can correspond to a physical dimension (e.g., anaverage length, width, or thickness) of the abrasive particles beingused in the mixture. When the mixture is deposited into the formingstructure 2100, the portions 2150 not only facilitate the placement ofthe abrasive particles between the portions 2150, but the portions 2150also facilitate the orientation of the abrasive particles, bypositioning the abrasive particles in a lying flat configuration with amajor surface of the abrasive particles lying parallel to a majorsurface of the final fixed abrasive article. The portions 2150 alsofacilitate the orientation of the abrasive particles such that a longestdimension of the abrasive particles and/or a major surface of theabrasive particles is positioned at a 45° angle to a side surface of theforming structure 2100 and, ultimately, a side surface of the finalfixed abrasive article. An exemplary image of a mixture of precursorbond material and abrasive particles residing in the forming structure2100 between the portions 2150 positioned at a 45° angle is depicted inFIG. 21D.

Furthermore, depending on the intended grinding direction of the finalfixed abrasive article, the abrasive particles being positioned at a 45°angle to a side surface of the abrasive article also can have a positiverake angle (e.g., +45° angle) or a negative rake angle (e.g., −45°angle). For example, if the abrasive particles are positioned at a 45°angle, and the angle inclines the abrasive particles in the intendedgrinding direction, then the abrasive particles have a positive rakeangle. If the abrasive particles are positioned at a 45° angle, and theangle inclines the abrasive particles opposite to the intended grindingdirection, then the abrasive particles have a negative rake angle.

FIG. 12B includes a top-down illustration of a forming structure 1205according to an embodiment. As illustrated, the forming structure 1205can have a plurality of openings 1221, 1222 and 1223 having variousshapes and sizes relative to each other. Moreover, as illustrated, theforming structure 1205 can have a variety of different orientations ofthe openings 1221-1223 relative to each other. It will be appreciatedthat the openings 1221-1223 may have a particular shape to control thepredetermined position and/or predetermined rotational orientation ofthe abrasive particles as the abrasive particles pass through theopenings 1221-1223. In more particular terms, for example, the openings1221 and 1223 may allow only abrasive particles having a triangulartwo-dimensional shape of a particular size range to pass through theforming structure 1205 in those particular locations, and thus controlthe predetermined position and/or predetermined rotational orientationof the abrasive particles passing therethrough on or within theprecursor bond material 1203. The openings 1222 may be sized and shapedto allow passage of certain types of abrasive particles therethroughincluding, for example, shaped abrasive particles having a rectangulartwo-dimensional shape of a particular size range.

In accordance with an embodiment, the openings 1221-1223 within theforming structure 1205 can have a particular two-dimensional shapeselected from the group consisting of a polygon, ellipsoids, irregularpolygons, Greek alphabet characters, Latin alphabet characters, Russianalphabet characters, complex shapes having a combination of polygonalshapes, shapes with a combination of linear and arcuate sections, and acombination thereof. Notably, the openings 1221-1223 can havesubstantially the same two-dimensional shape as a two-dimensional shapeof the shaped abrasive particles and/or elongated abrasive particlespassing there through. In addition, the two-dimensional shape of theopenings 1221-1223 can facilitate selective passage of only shapedabrasive particles of the desired shape and size through the openingsand thus selectively controlling the predetermined position,predetermined rotational orientation, type and size of the abrasiveparticle placed on or within the precursor bond material 1203.

Moreover, the placement of the openings 1221-1223 within the formingstructure 1205 can facilitate placement of the abrasive particles in acontrolled distribution on or within the precursor bond material 1203,and therefore, in the finally-formed fixed abrasive article. As, furtherillustrated in FIG. 12C, the openings 1221-1223 can be arranged invarious configurations including a controlled distribution. Moreover, itwill be appreciated that the openings 1221-1223 can be arranged within aparticular distribution that can further define the distribution ofabrasive particles on the precursor bond material 1203. As will beappreciated, the distribution of the openings 1221-1223 can correspondto and define the controlled distribution of at least a portion of theabrasive particles within the precursor bond material 1203 and thefinally-formed fixed abrasive article. In one embodiment, the openings1221-1223 can be staggered relative to each other and relative to agiven radial axis. That is, the openings 1221-1223 can be placed inconcentric rings, but at different radial distances, from the center ofthe forming structure 1205, as is shown in FIG. 12C. At least some ofthe openings in one concentric ring (e.g., the openings 1221 positionedat one radial distance from the center of the body) also can bestaggered (not shown) relative to at least some of the openings in theother concentric rings (e.g., the openings 1222 and 1223 positioned atlesser radial distances from the center of the body). As a result, thestaggered openings 1221-1223 would occupy different positions alongdifferent radial axes of the body or be staggered in their positionsrelative to each radial axis. The abrasive particles which pass throughthe staggered openings 1221-1223 of the forming structure 1205 candefine a controlled, non-shadowing arrangement in the final fixedabrasive article.

In an alternative embodiment, the openings 1221-1223 can be blindopenings or pockets defining a space within the body of the formingstructure 1205, which do not extend completely through the thickness ofthe forming structure 1205. Still, each of the openings 1221-1223 can bearranged, sized, and shaped to contain a shaped abrasive particle and/orelongated abrasive particle and selectively control the predeterminedposition, predetermined rotational orientation, type and size of theabrasive particle placed on or within the precursor bond material 1203.Notably, in the instance where the forming structure 1205 utilizesopenings 1221-1223 in the form of pockets, the openings 1221-1223 canfirst be filled with a suitable number of shaped abrasive particlesand/or elongated abrasive particles. The forming structure 1205 can thenbe delivered to a precursor bond material 1203 and inverted such that atleast one surface of the shaped abrasive particles and/or elongatedabrasive particles contained within the openings 1221-1223 contacts asurface of the precursor bond material 1203. The forming structure 1205may then be lifted leaving the shaped abrasive particles and/orelongated abrasive particles on the precursor bond material 1203, andthe abrasive particles may have a predetermined position, predeterminedrotational orientation, and/or controlled distribution on the precursorbond material 1203 as provided by the openings 1221-1223 in the formingstructure. The single layer of a plurality of abrasive particles (e.g.,shaped abrasive particles and/or elongated abrasive particles) overlyingthe precursor bond material 1203 can define a fixed abrasive preform.One or more preforms can be made separately and then combined to form agreen body of an abrasive article. The green bond can be treatedaccording to any one of the methods herein, including for example,pressing (e.g., cold pressing, warm pressing, hot pressing, etc.) tochange the green body to a finally formed abrasive article.

Referring to FIG. 9, the process can further include step 903, duringwhich the green body formed in step 902 is treated to form a fixedabrasive article. The process of treating can include treating theprecursor bond material to form a finally-formed bond material. Treatingmay be selected from the group of processes including, but not limitedto, heating, curing, sintering, melting, oxidizing, reducing, radiating,cooling, freezing, and a combination thereof. Moreover, as noted herein,any of the foregoing treating processes may be conducted completely orpartially at any point during the forming process to facilitate theformation of a fixed abrasive article of the embodiments herein.

In an embodiment, the forming structure may be a temporary structurethat is not part of the finally-formed fixed abrasive article. Forexample, referring again to the forming structure 1205 of FIG. 12A, theforming structure 1205 may be in the form of a plate configured tocontrol the predetermined position and/or predetermined rotationalorientation of the abrasive particles as they are placed on theprecursor bond material 1203. The forming structure 1205 is removedprior to final treatment of the bond material to form the finally-formedfixed abrasive article. In such instances, the abrasive particles may betemporarily in contact with the forming structure 1205 during theforming process, but the forming structure may be removed prior to finalprocessing. In accordance with an embodiment, the forming structure 1205can include a material such as a metal, organic material, resin,polymer, glass, ceramic, monocrystalline material, polycrystallinematerial, natural material such as mineral, synthetic material, and acombination thereof.

In yet another embodiment, the forming structure can be an integratedstructure contained within the finally-formed fixed abrasive article.For example, referring to FIG. 13, a system 1301 for forming a fixedabrasive article using a forming structure is provided in accordancewith an embodiment. The system 1301 can include a production tool 1302,a precursor bond material 1303, and abrasive particles 1304 connected toeach other via a forming structure 1305. In such instances, the formingstructure 1305 can be a permanent structure configured to connect andcouple at least a portion of the abrasive particles 1304 to each other.In such instances, the forming structure 1305 may be referred to as anorientation structure in the finally-formed fixed abrasive, wherein theabrasive particles 1304 can be permanently attached to the formingstructure 1305 and have a predetermined position and/or predeterminedrotational orientation based on their attachment to the formingstructure 1305. As such, further processing may include deposition ofprecursor bond material over the abrasive particles 1304 and formingstructure 1305 such that the forming structure 1305 is integrated withinthe finally-formed fixed abrasive article.

In accordance with an embodiment, the forming structure 1305 can includea material such as a metal, an organic material, a resin, a polymer, aglass, a ceramic, a monocrystalline material, a polycrystallinematerial, a natural material such as a mineral, a synthetic material,and a combination thereof.

In one embodiment, the forming structure 1305 can be a network structureincluding abrasive particles coupled to each other. For example, theforming structure can include bridges 1305 which, in one embodiment, canbe akin to the orientation structure 821 depicted in FIG. 8. As notedherein, in certain instances, the bridges 1305 of the forming structure1305 can be a permanent part of the fixed abrasive article. However, inan alternative embodiment, the bridges 1305 of the forming structure1305 may be temporary and the finally-formed fixed abrasive article canbe essentially free of the bridges 1305 of the forming structure 1305.In such instances, the bridges 1305 may be consumed or removed duringprocessing to form the fixed abrasive article. For example, the bridges1305 of the forming section 1305 connecting the abrasive particles 1304may be removed during treating of the green body, such as during aheating process. For example, one process may include volatilization ofthe bridges 1305, such that the bridges 1306 are evolved as a gas orform porosity within the finally-formed fixed abrasive article.

In other instances, the forming structure 1305 including the bridges1305 coupling the abrasive particles to each other, may be made of amaterial that is similar to the precursor bond material 1303. In someembodiments, this may facilitate absorption of at least a portion of theforming structure 1305, such as the bridges 1305, during treatment. Assuch, at least a portion of the forming structure 1305 can be integratedinto the precursor bond material and become part of the fixed abrasivearticle during the treating process. In one particular embodiment, atleast a portion of the forming structure 1305, such as the bridges 1305,can be dissociated or absorbed during treatment of the precursor bondmaterial 1303 to form the finally-formed bond material and thefinally-formed fixed abrasive article.

In yet another embodiment, the forming structure may include at leastone structure configured to allow the flow of a mixture including theprecursor bond material and abrasive particles through one or moreopenings in the forming structure to control the deposition of theprecursor bond material and abrasive particles. For example, FIG. 14includes an illustration of a system for forming a fixed abrasivearticle according to an embodiment. As illustrated, the system 1401 caninclude a production tool 1402 and deposition of a precursor bondmaterial 1403 within the production tool 1402. In certain instances, thesystem may utilize multiple forming structures, including a firstforming structure 1420, which may have a reservoir for holding theprecursor bond material 1421 therein until it is deposited as a layer ofprecursor bond material 1403.

As further illustrated, a forming structure 1410 can also be utilizedand facilitate deposition of a mixture 1413 including abrasive particles1412 and precursor bond material 1411 that may be deposited through anopening of a nozzle 1431 of the forming structure 1410 in a manner tocontrol the predetermined position and/or predetermined rotationalorientation of the abrasive particles 1404. The opening of the nozzle1431 can be sized and shaped to facilitate suitable deposition of theabrasive particles 1412 and precursor bond material 1411 in the desiredmanner. According to one embodiment, the mixture 1413 can be a wetmixture that is poured through at least one opening in the formingstructure 1410. In another embodiment, one or more forces may be appliedto the mixture 1413 within the forming structure 1410 to facilitatedeposition of the mixture 1413. The mixture 1413 can be deposited as alayer of precursor bond material 1405 and abrasive particles 1404,wherein the abrasive particles 1404 can have a predetermined rotationalorientation relative to a side surface of the production tool 1402 and,ultimately, the finally-formed fixed abrasive article.

The forming structures of the embodiments herein also can be configuredto control the predetermined tilt angle of at least a portion of theabrasive particles in the finally-formed fixed abrasive article. Assuch, the forming structure can be configured to control the averagepredetermined tilt angle and standard deviation of the predeterminedtilt angle of a portion of the abrasive particles as described inembodiments herein.

FIG. 15 includes a flowchart providing a method of forming a fixedabrasive article according to an embodiment. As illustrated, the processcan be initiated at step 1501 by forming a mixture including a precursorbond material. The precursor bond material can include those materialsas noted in embodiments herein.

The process can continue with step 1502 by depositing abrasive particlesinto the precursor bond material to form a green body. As will beappreciated, the abrasive particles can include shaped abrasiveparticles and/or elongated abrasive particles as described inembodiments herein.

In accordance with at least one embodiment, the process of depositingthe abrasive particles can include forming the abrasive particles. Thatis, the abrasive particles can be formed during the process of formingthe fixed abrasive article. In one particular embodiment, the abrasiveparticles can be formed in situ during the process of forming the entirefixed abrasive article. For example, in one instance, the process caninclude forming a first portion of abrasive particles, depositing afirst portion of the precursor material on the first portion abrasiveparticles, and thereafter forming a second portion of abrasiveparticles, distinct from the first portion of abrasive particles, on thefirst portion of the precursor bond material. As will be appreciated,the first and second portions of abrasive particles can include a firstgroup in a radial plane, first and second groups in different radialplanes, a first radial set, first and second radial sets, a first axialcollection, first and second axial collections, a first axial set, firstand second axial sets, and a combination thereof. As will beappreciated, the process of forming the first portion of abrasivearticles can include forming a first portion including shaped abrasiveparticles and/or elongated abrasive particles having a predeterminedposition and/or predetermined rotational orientation relative to a sidesurface of the production tool that may define the side surface of thefinally-formed fixed abrasive article.

Certain suitable forming processes to form the abrasive particles caninclude an additive manufacturing process, printing, screen printing,shaping, casting, stamping, molding, scoring, fracturing, drying, and acombination thereof. In a particular embodiment, such as illustrated inFIG. 16, a system 1601 for forming a fixed abrasive article according toan embodiment can include a production tool 1602 and a precursor bondmaterial 1603. The system 1601 further includes a deposition structure1605 such as a deposition head 1606 configured to form the abrasiveparticles 1604 in situ on the precursor bond material 1603. For example,as illustrated in FIG. 16, discrete abrasive particles, including theabrasive particle 1607, can be formed on or within the precursor bondmaterial 1603 by the deposition structure 1605. In one embodiment, thedeposition structure 1605 can include a 3-D printing device such thatthe forming process includes 3-D printing of the abrasive particlesduring the forming of the fixed abrasive article. It will be appreciatedthat 3-D printing can include 3-D printing of shaped abrasive particlesand/or elongated abrasive particles. Moreover, while a single depositionstructure 1605 is illustrated, it is contemplated that a plurality ofdeposition structures or a single deposition structure with a pluralityof deposition heads may be utilized to simultaneously form a pluralityof abrasive particles.

The process of forming the fixed abrasive article can further includeforming abrasive particles and creating a forming structure (e.g., anorientation structure) configured to be coupled to the abrasiveparticles. As such, the forming process can include formation ofabrasive particles and one or more forming structures, which may havebridges 1612 coupling abrasive particles to each other. In certaininstances, one or more groups of abrasive particles 1604 and bridges1612 can be coupled to each other, wherein the bridges 1612 of theforming structure can facilitate holding the abrasive particles 1604 ina predetermined position and/or predetermined rotational orientationduring the forming process and within the finally-formed fixed abrasivearticle. Notably, the forming structure including the bridges 1612extending between the abrasive particles 1604 can be formed by 3-Dprinting or any of the other processes noted herein. For example, asfurther illustrated in FIG. 16, the deposition head 1605 can include a3-D printing head configured to form the bridges 1612 of the formingstructure that extend between at least a portion of the abrasiveparticles 1604. It will be appreciated that the process of forming theabrasive particles and the forming structure together is an alternativeprocess and need not necessarily always occur.

In yet another embodiment, the process of forming the abrasive particlesduring the process of forming the fixed abrasive article can include ascreen printing process. That is, forming can include screen printingabrasive particles having a predetermined position and/or apredetermined rotational orientation on the precursor bond material.FIG. 17A includes a system of forming a fixed abrasive article accordingto an embodiment. The system 1701 can include a production tool 1702including a precursor bond material 1703 and precursor abrasiveparticles 1704 being formed within openings of a screen 1705 during ascreen printing process. As further illustrated in FIG. 17B, afterforming the precursor abrasive particles 1704 in the process of FIG.17A, the screen 1705 can be removed such that precursor abrasiveparticles 1704 are overlying the precursor bond material 1703.

The precursor abrasive particles that are formed during the process offorming the fixed abrasive article can undergo further processing toform finally-formed abrasive articles. Some suitable forming processescan include heating, curing, drying, doping, cooling, freezing, coating,sintering, and a combination thereof. In at least one embodiment, theprocess of treating the precursor shaped abrasive particles andformation of finally formed abrasive particles can be the same processthat may be used to treat the precursor bond material and form afinally-formed bond material of the finally-formed fixed abrasive.Still, in alternative instances, the process of treating the precursorshaped abrasive particles to form final abrasive particles can be adifferent process than the process used to treat the precursor bondmaterial to form a finally-formed bond material of the finally-formedfixed abrasive.

In accordance with another embodiment, the process of depositing theabrasive particles on or within the precursor bond material can furtherinclude rearranging at least a portion of the abrasive particles to havea predetermined position and/or predetermined rotational orientation.For example, as illustrated in the process of FIG. 18, a system 1801 caninclude a production tool 1802 and a precursor bond material 1803 formedaccording to an embodiment herein. As further illustrated, the abrasiveparticles 1804 can be deposited on the precursor bond material 1803.Thereafter, the abrasive particles 1804 may be rearranged to change thepredetermined position and/or the predetermined rotational orientationof the abrasive particles. In certain instances, rearranging can includeproviding a force to the abrasive particles 1804, which force isconfigured to cause a change in the predetermined position and/orrotational orientation of the abrasive particles 1804. For example, inone embodiment, a rotational force 1805 and/or vibrational force 1805may be applied to the production tool 1802 to facilitate a change in thepredetermined position and/or predetermined rotational orientation ofthe abrasive particles 1804 on or within the precursor bond material1803. Some suitable forces that may be utilized can include gravity,centripetal, centrifugal, uniaxial, biaxial, isometric, and acombination thereof.

Alternatively, the process of rearranging the abrasive particles caninclude providing energy to the abrasive particles configured to cause achange in the predetermined position and/or predetermined rotationalorientation of the abrasive particles on or within the precursor bondmaterial. For example, as illustrated in FIG. 18, in certain instances,an electromagnetic energy 1806 may be applied to the abrasive particles1804 to facilitate rearranging the abrasive particles on or within theprecursor bond material 1803. The abrasive particles may include amaterial or may be coated with a material (e.g., silane) that canfacilitate their alignment by the application of electromagnetic energy.Other suitable forms of energy that may be supplied to the abrasiveparticles 1804 can include electrical, mechanical, vibratory,electromagnetic, magnetic, sonic, and a combination thereof. Whilereference has been made to deposition of the abrasive particles andrearrangement of the abrasive particles after deposition, it will beappreciated that the process of rearrangement may be conducted duringthe process of deposition, such as before the abrasive particles 1804contact the precursor bond material 1803.

In yet another embodiment, the process of depositing the abrasiveparticles can include deposition of a mixture of the abrasive particlesand precursor bond material into the production tool. FIG. 19 includes asystem for forming a fixed abrasive article according to an embodiment.As illustrated, the system 1901 can include deposition of a mixture 1903into a production tool 1902, where the mixture includes the precursorbond material 1904 and abrasive particles 1905. After deposition of themixture 1902, one or more forces can be applied to the mixture 1902 tofacilitate a change in the position and/or rotational orientation of theabrasive particles, such that the abrasive particles are urged to apredetermined position and/or predetermined rotational orientation ofthe abrasive particles. In one particular embodiment, the process ofapplying a force can include translating one or more structures 1906(e.g., a doctor blade), such as in the direction 1907, over the surfaceof the mixture 1903 to facilitate the change in position and/orrotational orientation of the abrasive particles 1905 from thoseillustrated in the region 1908 to those illustrated in the region 1909.

FIG. 20 includes an illustration of a system for forming a fixedabrasive article according to an embodiment. As illustrated, the system2000 can include a production tool 2016 and a mixture 2006, includingprecursor bond material 2003 and abrasive particles 2004. The mixture2006 is contained in and deposited by a deposition structure 2010through a forming structure 2002.

In particular instances, deposition of the mixture 2006 can include oneor more processes such as printing (e.g., screen-printing), molding,pressing, casting, sectioning, cutting, dicing, punching, pressing,drying, curing, coating, extruding, rolling, and a combination thereof.In a particular embodiment, deposition includes extruding the mixture2006 through a forming structure 2002.

The forming structure 2002 can include one or more openings. Theopenings can be sized and shaped to allow the flow of the mixture 2006therethrough and orientation of the abrasive particles 2004 therein. Thesize, shape, and distribution of the openings in the forming structure2002 can be controlled to facilitate a deposition of the abrasiveparticles 2004 with a predetermined position, a controlled distribution,and/or a predetermined rotational orientation relative to a side surfaceof the production tool 2016 and, ultimately, a major surface of thefinally-formed fixed abrasive article. While not illustrated, it iscontemplated that more than one type of forming structure can beutilized to create different portions within the fixed abrasive article,where the different portions of the article include abrasive particlesof different abrasive characteristics and/or orientationcharacteristics, including, but not limited to, predetermined positionand/or predetermined rotational orientation.

In an embodiment, the openings in the forming structure 2002 may have atwo-dimensional shape selected from the group consisting of a polygon,an ellipsoid, a numeral, a Greek alphabet character, a Latin alphabetcharacter, a Russian alphabet character, a complex shape having acombination of polygonal shapes, and a combination thereof. In anotherembodiment, the openings in the forming structure 2002 may have a sametwo-dimensional shape as the two-dimensional shape of the abrasiveparticles 2004.

Deposition of the mixture 2006 can form a plurality of preformed bodies2014, which bodies can include abrasive particles 2004 and precursorbond material 2003, and which bodies also can have different or similarshapes and sizes. In an embodiment, all of the preformed bodies 2014 mayhave any number of same, or similar, characteristics, such as forexample, dimensions, shapes, homogeneity, or abrasive particle density.

In an embodiment, the preformed bodies 2014 may each include anelongated preformed structure. In a particular instance, each of thepreformed bodies 2014 may be in the form of a pellet or another objecthaving a predetermined shape.

The preformed bodies 2014 can each have a length (as shown by thedimension “L” in FIG. 20) and a maximum width, as measured in adirection perpendicular to the length and as shown by the dimension “W”in FIG. 20. In an embodiment, the maximum width of at least one of thepreformed bodies 2014 may be a diameter of the at least one preformedbody 2014. In a particular embodiment, the length may be at least 25% ofthe maximum width, such as at least 100% of the maximum width, at least150% of the maximum width, at least 175% of the maximum width, at least200% of the maximum width, at least 250% of the maximum width, or atleast 500% of the maximum width. The preformed bodies 2014 also may havean aspect ratio, as measured by a ratio of the length to the width ormaximum diameter, of at least 0.1, such as at least 0.2, at least 0.5,at least 1, at least 1.5, at least 2, at least 3, at least 4, at least5, at least 6, at least 7, at least 8, at least 9, or at least 10. Inanother embodiment, the preformed bodies 2014 may have an aspect ratioof less than 100, such as less than 50, or less than 25.

In certain instances, at least one of the preformed bodies 2014 may begenerally cylindrical. As used herein to describe the preformed bodies2014, “generally cylindrical” refers to a condition wherein at least oneof the preformed bodies 2014 may occupy at least 75% of a volume of abest fit cylinder, such as at least 80% of a volume of a best fitcylinder, such as at least 95% of a volume of a best fit cylinder, suchas at least 90% of a volume of a best fit cylinder, such as at least 95%of a volume of a best fit cylinder, such as at least 96% of the volumeof the best fit cylinder, at least 97% of the volume of the best fitcylinder, at least 98% of the volume of the best fit cylinder, or atleast 99% of the volume of the best fit cylinder. In a furtherembodiment, a majority of the preformed bodies 2014 may be generallycylindrical. In another embodiment, all of the preformed bodies 2014 maybe generally cylindrical. In other instances, at least one of thepreformed bodies 2014 may be cylindrical. That is, at least one of thepreformed bodies 2014 may have a first face, a second face parallel withrespect to the first face, and a cylindrical sidewall disposed betweenthe first and second faces. In a further embodiment, a majority of thepreformed bodies 2014 may be cylindrical. In another embodiment, all ofthe preformed bodies 2014 may be cylindrical.

In another embodiment, at least one of the preformed bodies 2014 mayhave a two-dimensional shape selected from the group consisting of apolygon, an ellipsoid, a numeral, a Greek alphabet character, a Latinalphabet character, a Russian alphabet character, a complex shape havinga combination of polygonal shapes, and a combination thereof.

The preformed bodies 2014 may have an abrasive particle density, asmeasured by a density of the abrasive particles 2004 relative to theoverall body of the preformed bodies 2014. In an embodiment, theabrasive particle density of the preformed bodies 2014 may be higherthan a conventional mixture of abrasive particles and precursor bondmaterial formed using a non-extrusion method or technique.

In certain instances, the abrasive particles 2004 may be homogenously,or nearly homogenously, distributed within at least one of the preformedbodies 2014. In another embodiment, the abrasive particles 2004 may berandomly or non-homogenously distributed within the preformed bodies2014.

In an embodiment, at least two of the abrasive particles 2004 disposedin at least one preformed body 2014 may have the same predeterminedthree-axis orientation with respect to one another. In anotherembodiment, at least two abrasive particles 2004 in each of thepreformed bodies 2014 may have the same predetermined three-axisorientation with respect to one another. In a further embodiment, allabrasive particles 2004 disposed in at least one of the preformed bodies2014 may have the same predetermined three-axis orientation with respectto one another. In yet another embodiment, all abrasive particles 2004disposed in each of the preformed bodies 2014 may have the samepredetermined three-axis orientation with respect to one another.

During or after deposition of the mixture 2006, the preformed bodies2014 may be combined, or positioned relative to one another, and treatedto form the fixed abrasive article. Additional precursor bond materialmay be applied prior to treating the preformed bodies 2014 and formingthe fixed abrasive article.

In accordance with another embodiment, the process of depositing themixture 2006 can further include rearranging at least a portion of thepreformed bodies 2014 within the production tool 2016. In an embodiment,the preformed bodies 2014 can be rearranged to abut one another. Inanother embodiment, all of the preformed bodies 2014 may be deposited ona surface of the production tool 2016 with little or no spacing betweenthe preformed bodies 2014. In a particular instance, at least two of thepreformed bodies 2014 may be deposited by the forming structure 2002 soas to be in at least partial contact with one another. In anotherparticular instance, a majority, such as all, of the preformed bodies2014 may be deposited so that each preformed body 2014 is in at leastpartial contact with an adjacent preformed body 2014. Any of theforegoing methods of formation may be combined with any of the othermethods to facilitate the formation of a fixed abrasive articleincluding abrasive particles having the features of the embodimentsherein. Notably, any portion of the foregoing methods can be combinedwith any of the features and steps of any of the other processes tofacilitate formation of a fixed abrasive article having the features ofthe embodiments herein.

Some reference has been made in the embodiments herein to staggering ofparticles. In addition to controlling the placement and rotationalorientation of each of the abrasive particles in the bonded abrasivebody, it may also be advantageous to control the placement androtational orientation of the abrasive particles relative to each other.For example, based upon some empirical data, it has been noted thatcertain arrangements of the abrasive particles may facilitate improvedoperations of the abrasive article. Notably, it may be advantageous tostagger the particles relative to each other and relative to one or morereference planes or axes within the body to avoid excessive wear anddecreased abrasive capabilities of the abrasive article during use.

According to one embodiment, the abrasive particles within any plane,group, collection, or set can be arranged in a particular distributionrelative to each other. The distribution can be a pattern having shortrange order and long range order, wherein the long range order is basedon repetition of a smallest unit defining the short range order. Thedistribution may be a random distribution of abrasive particles havingno discernable short range order or long range order. In otherinstances, the distribution may be a controlled, non-uniformdistribution. A controlled “non-uniform distribution” means that theposition of the abrasive particles has a controlled asymmetry (i.e., acontrolled randomness), such that although the distribution of abrasiveparticles can be described by or predicted by, for example, a radial,spiral, or phyllotactic equation, the distribution of abrasive particlesexhibits at least a partial asymmetry. The controlled non-uniformdistribution can be partially, substantially, or fully asymmetric. Thecontrolled non-uniform distribution can be utilized for a portion ofabrasive particles within any plane, group, collection, and/or set. Thedistribution can cover multiple portions of the abrasive article or cancover only a portion of the abrasive article.

It is contemplated that the controlled non-random distributionsaccording to the embodiments described herein can also include adistribution where only a portion of the total number of abrasiveparticles of the distribution possesses a controlled asymmetry. Such asituation can occur, for instance, by combining or substituting aportion of a uniformly distributed pattern or a completely randompattern with a portion of the controlled non-uniform distribution.Still, in at least one embodiment, the controlled non-randomdistribution can include a distribution where 100% of the particleshaving a controlled asymmetry.

The controlled asymmetry can be a controlled reflection asymmetry (alsocalled mirror symmetry, line symmetry, and bilateral symmetry), acontrolled rotational asymmetry, a controlled translational symmetry,controlled glide reflection symmetry, or combinations thereof. In atleast one embodiment, the non-uniform distribution can be an arrangementdescribed by a rotational asymmetry. For example, for a radial, spiral,or phyllotactic pattern having a rotational symmetry of an order of one,such a distribution has no rotational symmetry because the distributionrepeats itself only once during a rotation of 360° about its center. Inother words, if two copies of the same exact pattern are placed directlyover each other and one copy is held constant while the second copy isrotated 360° about its center, all of the apertures of both copies willcome into alignment only once during the 360° rotation.

In one embodiment, the distribution can be a phyllotactic pattern. Asused herein, “a phyllotactic pattern” means a pattern related tophyllotaxis. Phyllotaxis is the arrangement of lateral organs such asleaves, flowers, scales, florets, and seeds in many kinds of plants.Many phyllotactic patterns are marked by the naturally occurringphenomenon of conspicuous patterns having arcs, spirals, and whorls. Thepattern of seeds in the head of a sunflower is an example of thisphenomenon. Multiple arcs or spirals, also called parastichy, can havetheir origin at a center point of the distribution and travel outward,while other spirals originate to fill in the gaps left by the innerspirals. See Jean's Phyllotaxis A Systemic Study in Plant Morphogenesisat p. 17. Frequently, the spiral-patterned arrangements can be viewed asradiating outward in both the clockwise and counterclockwise directions.

FIG. 25A provides a top-down illustration of a portion of an abrasivearticle according to an embodiment. Notably, FIG. 25A includes anillustration of a radial plane 2501 within an abrasive article. Theradial plane 2501 includes shaped abrasive particles 2502 each having atriangular two-dimensional shape as viewed in the plane of the radialplane 2501. As illustrated, each of the abrasive particles issubstantially laying down within the radial plane 2501. FIG. 25A is anillustration of a distribution of abrasive particles having acontrolled, non-random distribution in the form of a phyllotacticpattern.

FIGS. 25B-D include images of other distributions that may be used tocontrol placement and rotational orientation of the abrasive particlesin a plane, group, set, or collection, such that the abrasive particlesare arranged in a particular distribution within the body of theabrasive article. Each of the distributions illustrated in FIGS. 25B-Dcan represent distributions of abrasive particles that may occur in anyplane, group, set, or collection within the embodiments herein. Each ofthe dots in the images of FIGS. 25B-D can represent the placement of anabrasive particle, such as a shaped abrasive particle and/or elongatedabrasive particle. The distributions illustrated in FIGS. 25B-D may alsorepresent a corresponding distribution of cavities for a form orproduction tool used to place the abrasive particles in the body of theabrasive article.

Moreover it will be appreciated that any of the distributionsillustrated in the figures herein can be used together or separately.For example, in one embodiment, it may be advantageous to utilize afirst type of distribution (e.g., the distribution of FIG. 25B) for afirst portion of abrasive particles (e.g., shaped abrasive particlesand/or elongated abrasive particles in a plane, group, collection, orset) and a second type of distribution (e.g., the distribution of FIG.25C) for a second portion of abrasive particles (e.g., shaped abrasiveparticles and/or elongated abrasive particles in a plane, group,collection, sector, or set).

Additionally, any one of the distributions provided herein can utilizedifferent groups of abrasive particles where the abrasive particles ofone group have at least one abrasive characteristic that is differentcompared to abrasive particles of another group. For example, theabrasive article may include a distribution including a first group ofabrasive particles and a second group of abrasive particles, wherein thefirst group and second group have at least one abrasive characteristicthat is distinct from each other. Suitable examples of abrasivecharacteristics include hardness, composition, average particle size,average grain size, fracture toughness, two-dimensional shape, tipsharpness, tip angle, aspect ratio, or any combination thereof. Forexample, in one embodiment, a first portion of a distribution, such asthe spiral portion 2510 of FIG. 25B, can include a first type of shapedabrasive particle having a first two-dimensional shape and a secondportion of the distribution, such as the spiral portion 2511 of FIG. 25Bcan include a second type of abrasive particle, such as an elongatedparticle or a diluent particle (e.g., an unshaped abrasive particle). Itwill be appreciated that any portions of any distribution may utilizedifferent groups of abrasive particles where the groups have at leastone abrasive characteristic that is distinct from the abrasive particlesin another group.

Moreover, it will be appreciated that any two portions of a distributionmay utilize abrasive particles having a different orientationcharacteristic. Exemplary orientation characteristics can include apredetermined rotational orientation, a predetermined lateral axisrotational orientation, a predetermined vertical axis rotationalorientation, or any combination thereof. For example, a first portion ofa distribution (e.g., the spiral portion 2510) can include abrasiveparticles having a first predetermined rotational orientation and asecond portion of the distribution (e.g., the spiral portion 2511) caninclude abrasive particles having a second predetermined rotationalorientation that is different than the first predetermined rotationalorientation. It will be appreciated that other controlled orientationcharacteristics may differ between different portions of thedistribution. Controlling one or more orientation characteristics ofabrasive particles between two different portions of a distribution mayfacilitate efficient grinding and limit the wear of the abrasive articlethat may affect grinding performance and life.

It will also be appreciated that one or more orientation characteristicsmay differ between particles within the same portion. As described inembodiments herein, any portion of a distribution including, forexample, the spiral portion 2510, may include different groups ofabrasive particles, which may have different abrasive characteristicsand/or orientation characteristics with respect to each other.

It will also be appreciated that different regions of the abrasivearticle, such as different axial planes, radial planes, and the like,can utilize different distributions. For example, in one embodiment, afirst radial plane of the body can include a first distribution, such asthe distribution illustrated in FIG. 25B. And a second radial plane,which can be disposed under or over the first radial plane within thebody of the abrasive article may utilize a second distribution that isdifferent from the first distribution.

In still another embodiment, various regions within the abrasive bodymay utilize the same distribution. For example, a first radial plane anda second radial plane, which are separated from each other by some axialdistance, can utilize the same distribution, such as the distributionillustrated in FIG. 25B. In yet a more particular embodiment, it iscontemplated that the same distribution may be utilized in differentregions (e.g., radial plane) within the body of the abrasive, but thedistributions may be rotated relative to each other to facilitatesuitable staggering of the particles. For example, a first radial planemay utilize the distribution illustrated in FIG. 25B and a second radialplane overlying the first radial plane may utilize the samedistribution, but the distribution in the second radial plane can berotated relative to the distribution in the first radial plane, suchthat abrasive particles in the same positions within the twodistributions are not overlapping, but staggered relative to each otherwhen viewing the radial planes top down.

In still another embodiment, a portion of the abrasive article (e.g.,such as a group of abrasive particles in the same radial plane) mayinclude a combination of abrasive particles arranged in a particulardistribution combined with other particles having a random arrangement.For example, a first group of abrasive particles, such as shapedabrasive particles, may be present in a portion of the abrasive articleincluding, for example, within the same radial plane and distributed inthe manner as illustrated in FIG. 25B. A second group of abrasiveparticles, such as diluent particles, may then be deposited at positionsbetween the positions occupied by the first group of abrasive particles,such as within the gap regions 2512 between the spiral portions 2510 and2511 that are associated with the first group of abrasive particles.Filling gap regions that exist between the positions associated with aparticular distribution may facilitate improved grinding efficiency andmay further limit the wear of the abrasive article during operation ofthe abrasive article. It will be appreciated that such an article can beformed by first depositing the first group of abrasive particles in acontrolled manner according to any of the techniques described herein,and later depositing one or more other groups of abrasive particles inthe gap regions.

FIG. 26 includes a top-down illustration of a portion of an abrasivearticle according to an embodiment. As illustrated, the abrasive article2601 includes a side surface 2602 and abrasive particles 2603, 2604,2605, 2606 and 2607 (2603-2607) contained within a first radial plane.The abrasive article further includes abrasive particles 2643, 2644,2645, 2646 and 2647 contained in a second radial plane underlying thefirst radial plane. As further illustrated, the abrasive particle 2603is spaced apart from the side surface 2602 by a spacing distance 2623,which is measured as the shortest distance along the radial axis 2613between the side surface 2602 and a point on the abrasive particle 2603closest to the side surface 2602 when viewed top down. The abrasiveparticle 2604 also includes a spacing distance 2624 along the radialaxis 2614. The abrasive particle 2605 also includes a spacing distance2625 along the radial axis 2615. The abrasive particle 2606 alsoincludes a spacing distance 2626. This difference in spacing distancescan define a staggered relationship between each of the adjacentabrasive particles 2603-2606 within the first radial plane, such that asthe abrasive article 2601 wears along the side surface, fresh particlesare constantly exposed, which may facilitate improved efficiency andlife of the abrasive article.

The abrasive particles may also be staggered relative to each other indifferent radial planes. For example, as illustrated in FIG. 26, theabrasive particle 2643, which is underlying the abrasive particle 2603,can be staggered relative to the abrasive particle 2603, such that oneparticle is not completely underlying the other abrasive particle. Asillustrated in FIG. 26, as viewed top down, at least a portion of theabrasive particle 2643 is offset from the abrasive particle 2603, suchthat the particles are not in perfect axial alignment relative to eachother. Stated alternatively, as viewed top down and as shown, at least aportion of the abrasive particle 2643 is not underlying the abrasiveparticle 2603. Ensuring that at least a portion of the abrasiveparticles in different radial planes are not in alignment with oneanother and have an axially and radially staggered relationship withrespect to each other may facilitate improved efficiency and life of theabrasive article. It will be appreciated that when evaluating the axialand/or radial staggering of abrasive particles in different radialplanes, such staggering is to be measured between the closest twoparticles or two immediately adjacent particles that are separated fromeach other by the smallest axial distance. FIG. 26 further illustratesthe same relationship of axial and radial staggering for each of thepairs of abrasive particles, including abrasive particles 2604 and 2644,abrasive particles 2605 and 2645, abrasive particles 2606 and 2646, andabrasive particles 2607 and 2647.

It will further be appreciated that the radial and/or axial staggeringof abrasive particles may be controlled by controlling one or morerotational orientation characteristics of the abrasive particles. In yetanother embodiment, the radial and/or axial staggering of abrasiveparticles may be controlled by controlling one or more rake angles ofthe abrasive particles.

It will be appreciated that reference herein to any materials of thearticles of the embodiments includes forming the article essentiallyfrom any of the materials mentioned. Moreover, it will be appreciatedthat the foregoing description also contemplates that any of thearticles of the embodiments herein may be essentially free of anymaterials that are described as well as those materials that are notdescribed with any of the articles.

Many different aspects and embodiments are possible. Some of thoseaspects and embodiments are described herein. After reading thisspecification, skilled artisans will appreciate that those aspects andembodiments are only illustrative and do not limit the scope of thepresent invention. Embodiments may be in accordance with any one or moreof the items as listed below.

EXAMPLES Example 1

Sample wheels were formed to analyze how the use of a formationstructure affects (a) the placement of abrasive particles in apredetermined position and/or predetermined rotational orientation; and(b) the grinding performance of the sample wheel.

A comparative wheel sample was made containing commercially availablerod-shaped sintered bauxite abrasive particles (CS1). An image of therod-shaped sintered bauxite abrasive particles, used in both thecomparative sample CS1 and the sample S1 discussed herein, are shown inFIG. 21A. The comparative sample CS1 was formed using a conventionalprocess, namely by pouring a mixture of precursor bond material and therod-shaped particles into a mold to form a green body. Then the greenbody was treated (e.g., cured) to form the fixed abrasive article CS1with a diameter of approximately 16″.

A first wheel sample, S1, was formed in accordance with the embodimentsdescribed herein. The same mixture of precursor bond material androd-shaped sintered bauxite abrasive particles used to make theconventional wheel sample CS1 was also used to make the sample S1. Themixture was deposited into a production tool having a forming structure.An illustration of the forming structure is shown in FIG. 21B. It willbe appreciated that the forming structure 2100 depicted in FIG. 21B canbe employed in any of the processes or embodiments described herein, orused with any of the shaped abrasive particles or elongated abrasiveparticles described herein, to assist with placing shaped or elongatedabrasive particles in predetermined positions and/or predeterminedrotational orientations within a fixed abrasive article.

The first wheel sample S1 was made using the forming structure 2100depicted in FIG. 21B, including the “radial” configuration of slots 2150as shown in FIG. 21B. After the mixture was deposited into theproduction tool, a green body was formed. Then the green body wastreated (e.g., cured) to form the fixed abrasive article sample S1 witha diameter of approximately 16″.

FIGS. 22A and 22B depict cross-sectional images of the comparative wheelsample CS1 and first sample S1, respectively. The cross-sectional imageswere both taken in a plane parallel to the major surfaces of thesamples. An analysis was performed on these images to assess theorientation of the abrasive particles within the sample wheels. Thoseabrasive particles whose orientation was substantially “radial,” orwhose longest dimension was parallel to a radial axis of the wheel andperpendicular to a side surface of the wheel, were denoted in a lightercolor. Those abrasive particles whose orientation was substantially“90°,” or whose longest dimension was perpendicular to a radial axis ofthe wheel and parallel to a side surface of the wheel, were denoted in adark color.

FIG. 22C depicts a bar graph of the results of the image analysis on thewheels depicted in FIGS. 22A and 22B. The largest percentage of theabrasive particles in the sample CS1 were oriented in a “tangentialdirection,” where a longest dimension of the particle was substantiallyperpendicular to a radial axis of the wheel and substantially parallelto the side surface or a tangent to the side surface. By contrast, thelargest percentage of the abrasive particles in the sample S1 wereoriented in a “radial direction,” where a longest dimension of theparticle was substantially parallel to a radial axis of the wheel andsubstantially perpendicular to the side surface or a tangent to the sidesurface. Clearly, then, the use of a forming structure, including theforming structure 2100 with the slots 2150, can facilitate the formationof a fixed abrasive article having shaped abrasive particles orelongated abrasive particles in predetermined positions and/orpredetermined rotational orientations.

In addition to sample S1, a further wheel sample S2 was made inaccordance with embodiments described herein, notably using the formingstructure 2100 depicted in FIG. 21C with the “45°” configuration of theslots 2150. The sample S2 included the same precursor bond material andabrasive particles as the CS1 and S1 sample wheels. After the mixturewas deposited into the production tool (an exemplary image of which isdepicted in FIG. 21D), a green body was formed. Then the green body wastreated (e.g., cured) to form the fixed abrasive article sample S2 witha diameter of approximately 16″.

Samples S1 and S2 were used in a grinding test on a workpiece of cold304 stainless steel at a constant speed. The samples S1-S2 were testedat two different depths of cut (“DoC”), namely at 0.075″ and 0.1″. Thegrinding performance of the samples S1-S2, and particularly thecumulative Q-ratio (lb/lb) of each sample for each of the two DoC, wasmeasured and summarized in the bar graph depicted in FIG. 23.

As FIG. 23 shows, sample S1 had a better Q-ratio for a DoC of 0.075″than for a DoC of 0.1″. Sample S2 was tested in both a positive rakedirection and a negative rake direction. That is, sample S2 was testedin a grinding direction that corresponds to the 45° inclination of theabrasive particles in the sample S2 wheel (a positive rake direction).Sample S2 also was tested in a grinding direction that was opposite tothe 45° inclination of the abrasive particles in the sample S2 wheel (anegative rake direction). In the negative rake direction, sample S2 hada better Q-ratio for a DoC of 0.1″ than for a DoC of 0.075″. In thepositive rake direction, sample S2 had a better Q-ratio for a DoC of0.075″ than for a DoC of 0.1″. In particular, for the 0.075″ DoC, sampleS2 had an 18% separation in Q-ratio between the negative and positiverake directions. Clearly, then, the use of a forming structure thatfacilitates the positioning of shaped abrasive particles or elongatedabrasive particles in predetermined positions and/or predeterminedrotational orientations also can affect the grinding performance of theresulting fixed abrasive article.

Example 2

Thin wheels were formed to analyze how the use of a formation structureaffects the placement of abrasive particles in a predetermined positionand/or predetermined rotational orientation.

A first wheel sample, S3, was formed according to a conventionalprocess. The sample wheel S3 was a 3″× 1/16″ Type 41 wheel (e.g., a flatcutting wheel) with a target weight of 19.2 grams. A precursor bondmaterial was formed in an Erlich mixer by blending 184 grams of dryphenolic resin (Durez 29346) with 893.8 grams of finely chopped bulkmolding compound (“BMC”). For the abrasive particles, 1006.9 grams oftriangular shaped abrasive particles (as described in accordance withembodiments herein) were mixed with 254.6 grams of Nephaline syenite (atype of weak grain). To this, 54.5 grams of liquid resin (Durez LPR5%)was added to wet the abrasive particles. This wet particle mix was addedto the dry precursor bond material blend while stirring. The wheel wasthen formed in a production tool (e.g., a mold cavity) by placing afirst layer of reinforcing material in the bottom of the mold cavity.The reinforcing material was IPAC style 3321 phenolic-coated fiberglasswith paper on one face. Each of these fiberglass webs, with the paper,weighs approximately 0.94 grams. The IPAC layer was placed into the moldcavity with the paper facing the bottom of the mold cavity, so that thepaper faced to the outside of the final wheel. Approximately 18.5 gramsof the mixture that contained both the precursor bond material andshaped abrasive particles was deposited on top of the IPAC layer. Themixture of precursor bond material and shaped abrasive particles wasdeposited into the mold cavity such that the shaped abrasive particleswere randomly distributed and oriented throughout the mixture. A secondIPAC layer was placed on top of the mixture, again with the paper facingto the outside of what would become the final wheel. This green bodyconfiguration was cold pressed in the mold cavity at a pressure of 100bar with a 4 second dwell. The compressed wheel was cured under a forceof approximately 200 pounds using the following cycle: (a) a ramptemperature over 5 hours from approximately room temperature to 195° C.;(b) a hold at 195° C. for 3 hours and 20 minutes; and (c) a ramptemperature over 1.5 hours from 195° C. to 60° C. A CT scan of thesample S3 was performed and a cross-sectional image of sample S3, asviewed in a plane parallel to the major surfaces of the sample wheel S3,is shown in FIG. 24A. As FIG. 24A shows, the triangular shaped abrasiveparticles are randomly distributed or positioned within the wheel S3.The particles also have random rotational orientations relative to, forexample, a side surface of the wheel S3.

A second wheel sample, S4, was formed in accordance with the embodimentsdescribed herein. The sample wheel S4 was a 3″× 1/16″ Type 41 wheel(e.g., a flat cutting wheel) with a target weight of 19.2 grams. Thesample wheel S4 was a layered structure featuring two IPAC layers on theouter major surfaces of the wheel, and an alternating structure of 8grains sheets interspersed with a precursor bond material. The precursorbond material, which included 1.1 grams of dry phenolic resin powder(Durez 29346), 1.78 grams of Nepheline Syenite, and 0.6 grams of liquidphenolic resin (Durez LPR5%) was mixed by hand in a small bowl with aspatula.

Each grain sheet, which weighed approximately 1.68 grams (including 0.89grams of grain and 0.79 grams of BMC), was formed in accordance withembodiments described herein. A forming structure, namely a template,included openings that were pockets. An image of the template used tomake each grain sheet is shown in FIG. 24B. That is, the openings werepockets that defined a space within the body of the template and did notextend completely through the thickness of the template. Notably, thepockets were staggered from one concentric ring to the next, such thatwhen the sample S4 wheel was viewed from the top down, the shapedabrasive particles of one ring were staggered in their radial positionas compared to adjacent concentric rings of shaped abrasive particles.For each grain sheet, approximately 1 gram of shaped abrasive particles(e.g., the same triangular shaped abrasive particles used in samplewheel S3) was spread around the template while the template was rotatedand gently shaken from side to side. This rotation and vibration stepassisted in filling most of the pockets in the template with shapedabrasive particles. The particle placement was completed by usingtweezers to place a particle in any open pocket, replace any brokenparticles in pockets with whole or unbroken particles, and remove anyexcess particles from the non-pocket areas of the template. A circularlayer of BMC having an outer diameter of 3″ was then placed on top ofthe particles in the template. The BMC was pressed into the particles.Then the BMC and template in combination were turned over, after whichthe template was removed from the BMC. The shaped abrasive particlesremained on the BMC layer. The grain sheet was refrigerated betweenlayers of wax paper until all of the grain sheets were completed and thewheel was ready for assembly.

The wheel was formed in a production tool (e.g., a mold cavity) byplacing a first layer of IPAC reinforcing material in the bottom of themold cavity with the paper facing toward the eventual outer surface ofthe wheel. One grain sheet was placed on top of the IPAC layer. Then 0.5grams of the precursor bond material was sprinkled onto the surface ofthe grain sheet. A second grain sheet was placed into the mold cavity,and a further 0.5 grams of the precursor bond material was sprinkledonto the surface of the second grain sheet. This process continued until8 total grain sheets, with seven layers of precursor bond materialsprinkled in between, were deposited in the mold cavity. A final layerof IPAC reinforcing material was deposited in the mold cavity with thepaper facing toward the eventual outer surface of the wheel. Then thewheel was pressed, stacked, and cured under the same conditionsdescribed above with respect to sample S3.

A CT scan of the sample S4 was performed and two cross-sectional imagesof sample S4, as viewed in a plane parallel to the major surfaces of thesample wheel S4, are shown in FIGS. 24C-24D. As FIGS. 24C-24D show, thetriangular shaped abrasive particles occupy predetermined positionswithin the wheel S4. First, the triangular shaped abrasive particles arepositioned in a pattern of concentric rings. Second, the triangularshaped abrasive particles are positioned in a predetermined rotationalorientation relative to a side surface of the wheel S4. Theirpredetermined rotational orientation is akin to that orientation shownand discussed in relation to particles 502-506 in FIG. 5A. Moreparticularly, a significant portion of the particles in the wheel S4exhibit a predetermined rotational orientation angle of approximately 0°because the longitudinal axes of the particles align with radial axes ofthe wheel. Many of the particles also have a major surface or facealigned with a major surface of the wheel S4. Clearly, the Sample S4demonstrates control of both the positioning of shaped abrasiveparticles or elongated abrasive particles in predetermined positions andpredetermined rotational orientations within a finally-formed fixedabrasive article.

EMBODIMENTS Embodiment 1

A fixed abrasive article comprising:

a body including abrasive particles contained within a bond material,the abrasive particles including shaped abrasive particles or elongatedabrasive particles having an aspect ratio of length:width of at least1.1:1, each of the shaped abrasive particles or elongated abrasiveparticles having a predetermined position or a predetermined three-axisorientation.

Embodiment 2

A fixed abrasive article comprising:

a body having abrasive particles contained within a bond material, theabrasive particles including a plurality of shaped abrasive particles orelongated abrasive particles having an aspect ratio of length:width ofat least 1.1:1, each of the shaped abrasive particles or elongatedabrasive particles have a predetermined rotational orientation anglerelative to a side surface of the body.

Embodiment 3

A fixed abrasive article comprising:

a body having abrasive particles contained within a bond material, theabrasive particles including a plurality of shaped abrasive particles orelongated abrasive particles having an aspect ratio of length:width ofat least 1.1:1, wherein at least a portion of the abrasive particles arecoupled to an orientation structure extending throughout a portion ofthe bond material within the body.

Embodiment 4

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the bond material comprises a material selected from the groupconsisting of vitreous, polycrystalline, monocrystalline, organic,metal, and a combination thereof.

Embodiment 5

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a shape selected from the group consisting ofcylindrical, conical, cup-shaped, depressed center wheel, and acombination thereof.

Embodiment 6

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises an upper surface, a bottom surface, andwherein the side surface extends between the upper surface and thebottom surface.

Embodiment 7

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the abrasive particles are contained within a three-dimensionalvolume of the bond material.

Embodiment 8

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises at least one reinforcing member, wherein thereinforcing member is selected from a group consisting of a wovenmaterial, a non-woven material, a composite material, a laminatedmaterial, a monolithic material, a natural material, a syntheticmaterial, and a combination thereof.

Embodiment 9

The fixed abrasive article of Embodiment 8, wherein the reinforcingmaterial comprises a material selected from the group consisting of amonocrystalline material, a polycrystalline material, a vitreousmaterial, a glass, a ceramic, a metal, an organic material, an inorganicmaterial, and a combination thereof, wherein the reinforcing member

Embodiment 10

The fixed abrasive article of Embodiment 8, wherein the reinforcingmaterial extends for at least a portion of the entire width of the body,wherein the reinforcing material extends for a majority of the entirewidth of the body, wherein the reinforcing material extends for anentire width of the body.

Embodiment 11

The fixed abrasive article of Embodiment 8, wherein the reinforcingmaterial is substantially contained within the volume of the bondmaterial, wherein the reinforcing material is intersecting an exteriorsurface of the body, wherein the reinforcing material defines a majorsurface of the body.

Embodiment 12

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein each of the shaped abrasive particles or elongated abrasiveparticles having a predetermined position and a predetermined three-axisorientation.

Embodiment 13

The fixed abrasive article of Embodiment 12, wherein at least a portionof the shaped abrasive particles or at least a portion of the elongatedabrasive particles have substantially the same predetermined three-axisorientation relative to the side surface of the body.

Embodiment 14

The fixed abrasive article of the Embodiment 13, wherein thepredetermined three-axis orientation includes a predetermined rotationalorientation of each the abrasive particles relative to a side surface ofthe body.

Embodiment 15

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein each of the shaped abrasive particles comprises a cutting tip orcutting edge having a predetermined orientation relative to the sidesurface.

Embodiment 16

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a first group of abrasive particles within afirst radial plane within the body, each of the abrasive particles ofthe first group having a predetermined rotational orientation within thefirst radial plane relative to a side surface of the body.

Embodiment 17

The fixed abrasive article of Embodiment 16, wherein the first group ofabrasive particles includes shaped abrasive particles or elongatedabrasive particles.

Embodiment 18

The fixed abrasive article of Embodiment 16, wherein the abrasiveparticles of the first group of abrasive particles are arranged in acontrolled distribution relative to each other.

Embodiment 19

The fixed abrasive article of Embodiment 18, wherein the controlleddistribution includes an ordered distribution of the first group ofabrasive particles relative to each other within the first radial plane.

Embodiment 20

The fixed abrasive article of Embodiment 16, wherein the abrasiveparticles within the first group have a predetermined position havingsubstantially the same axial position within the radial plane withrespect to each other.

Embodiment 21

The fixed abrasive article of Embodiment 20, wherein the abrasiveparticles of the first group comprise a different radial position withrespect to each other.

Embodiment 22

The fixed abrasive article of Embodiment 16, wherein the abrasiveparticles of the first group have at least one abrasive characteristicthat is substantially the same, wherein the at least one abrasivecharacteristic is selected from the group consisting of hardness,composition, average particle size, average grain size, fracturetoughness, two-dimensional shape, tip sharpness, tip angle, aspectratio, and a combination thereof.

Embodiment 23

The fixed abrasive article of Embodiment 16, further comprising a secondgroup of abrasive particles within a second radial plane within thebody, each of the abrasive particles of the second group having apredetermined rotational orientation within the second radial planerelative to a side surface of the body.

Embodiment 24

The fixed abrasive article of Embodiment 23, wherein the second group ofabrasive particles includes shaped abrasive particles or elongatedabrasive particles.

Embodiment 25

The fixed abrasive article of Embodiment 23, wherein the second group ofabrasive particles are arranged in a controlled distribution relative toeach other.

Embodiment 26

The fixed abrasive article of Embodiment 25, wherein the controlleddistribution includes an ordered distribution of the second group ofabrasive particles relative to each other within the second radialplane.

Embodiment 27

The fixed abrasive article of Embodiment 23, wherein the first radialplane and second radial plane are axially spaced apart from each otherwithin the body.

Embodiment 28

The fixed abrasive article of Embodiment 23, wherein the first group ofabrasive particles have a first predetermined rotational orientation andthe second group of abrasive particles have a second predeterminedrotational orientation different than the first predetermined rotationalorientation.

Embodiment 29

The fixed abrasive article of Embodiment 23, wherein the abrasiveparticles within the second group have a predetermined position havingsubstantially the same axial position within the radial plane withrespect to each other.

Embodiment 30

The fixed abrasive article of Embodiment 29, wherein the abrasiveparticles of the second group comprise a different radial position withrespect to each other.

Embodiment 31

The fixed abrasive article of Embodiment 23, wherein the abrasiveparticles of the second group have at least one abrasive characteristicthat is the same, wherein the at least one abrasive characteristic isselected from the group consisting of hardness, composition, averageparticle size, average grain size, fracture toughness, two-dimensionalshape, tip sharpness, tip angle, aspect ratio, and a combinationthereof.

Embodiment 32

The fixed abrasive article of Embodiment 31, wherein the abrasiveparticles of the first group and the second group have at least oneabrasive characteristic that is different.

Embodiment 33

The fixed abrasive article of Embodiment 16, wherein the first group ofabrasive particles includes a first radial set of abrasive particlesspaced at a first radial distance from a center of the body.

Embodiment 34

The fixed abrasive article of Embodiment 33, wherein each of theabrasive particles of the first radial set of abrasive particles havesubstantially the same predetermined rotational orientation relative toeach other.

Embodiment 35

The fixed abrasive article of Embodiment 33, wherein each of theabrasive particles of the first radial set of abrasive particles havesubstantially the same predetermined rotational orientation relative toa side surface of the body.

Embodiment 36

The fixed abrasive article of Embodiment 33, wherein each of theabrasive particles of the first radial set of abrasive particles havesubstantially the same axial position with respect to each other, andare spaced at substantially the same first radial distance from thecenter of the body with respect to each other.

Embodiment 37

The fixed abrasive article of Embodiment 35, wherein the abrasiveparticles of the first radial set have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 38

The fixed abrasive article of Embodiment 33, wherein the first group ofabrasive particles includes a second radial set of abrasive particlesspaced at a second radial distance from a center of the body that isdifferent than the first radial distance.

Embodiment 39

The fixed abrasive article of Embodiment 38, wherein each of theabrasive particles of the second radial set of abrasive particles havesubstantially the same predetermined rotational orientation relative toeach other.

Embodiment 40

The fixed abrasive article of Embodiment 38, wherein at least two of theabrasive particles of the second radial set of abrasive particles have adifferent predetermined rotational orientation relative to each other.

Embodiment 41

The fixed abrasive article of Embodiment 38, wherein each of theabrasive particles of the second radial set of abrasive particles havesubstantially the same predetermined rotational orientation relative toa side surface of the body.

Embodiment 42

The fixed abrasive article of Embodiment 38, wherein the first radialset is positioned as initial abrasive elements configured to conductinitial material removal operations and the second radial set ispositioned as a back-up abrasive elements configured to conduct materialremoval operations after some portion of the first radial set is worn.

Embodiment 43

The fixed abrasive article of Embodiment 38, wherein the abrasiveparticles of the first radial set are closer to a side surface of thebody than the abrasive particles of the second radial set.

Embodiment 44

The fixed abrasive article of Embodiment 38, wherein the abrasiveparticles of the first radial set intersect a side surface of the bodyand the abrasive particles of the second radial set are spaced adistance from the side surface.

Embodiment 45

The fixed abrasive article of Embodiment 38, wherein each of theabrasive particles of the second radial set of abrasive particles havesubstantially the same axial position with respect to each other, andare spaced at substantially the same second radial distance from thecenter of the body with respect to each other.

Embodiment 46

The fixed abrasive article of Embodiment 38, wherein the abrasiveparticles of the second radial set have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 47

The fixed abrasive article of Embodiment 46, wherein the abrasiveparticles of the first radial set have at least one abrasivecharacteristic different than the abrasive particles of the secondradial set.

Embodiment 48

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a plurality of groups of abrasive particlesassociated with a plurality of different radial planes within the body,and wherein each group of the plurality of groups of abrasive particlesincludes a plurality of radial sets of abrasive particles, wherein eachof the radial sets are spaced at a different radial distance from acenter of the body relative to each other.

Embodiment 49

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a plurality of axial collections of abrasiveparticles, wherein each axial collection includes a plurality ofabrasive particles contained within a same axial plane within the body.

Embodiment 50

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a first axial collection of abrasiveparticles within a first axial plane within the body, each of theabrasive particles of the first axial collection having a predeterminedrotational orientation relative to a side surface of the body.

Embodiment 51

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the first axial collection include shaped abrasiveparticles or elongated abrasive particles.

Embodiment 52

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the first axial collection of abrasive particles arearranged in a controlled distribution relative to each other.

Embodiment 53

The fixed abrasive article of Embodiment 52, wherein the controlleddistribution includes an ordered distribution of the first axialcollection of abrasive particles relative to each other within the firstaxial plane.

Embodiment 54

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the first axial collection have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 55

The fixed abrasive article of Embodiment 50, further comprising a secondaxial collection of abrasive particles within a second axial planewithin the body that is different than the first axial plane, each ofthe abrasive particles of the second axial collection having apredetermined rotational orientation within the second axial planerelative to a side surface of the body.

Embodiment 56

The fixed abrasive article of Embodiment 55, wherein the abrasiveparticles of the second axial collection include shaped abrasiveparticles or elongated abrasive particles.

Embodiment 57

The fixed abrasive article of Embodiment 55, wherein the second axialcollection of abrasive particles are arranged in a controlleddistribution relative to each other.

Embodiment 58

The fixed abrasive article of Embodiment 57, wherein the controlleddistribution includes an ordered distribution of the second axialcollection of abrasive particles relative to each other within thesecond axial plane.

Embodiment 59

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the second axial collection have a predetermined positionincluding substantially the same angular position within the body.

Embodiment 60

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the second axial collection have a different radialposition with respect to each other.

Embodiment 61

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the second axial collection have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 62

The fixed abrasive article of Embodiment 50, wherein the abrasiveparticles of the first axial collection have at least one abrasivecharacteristic different than the abrasive particles of the second axialcollection.

Embodiment 63

The fixed abrasive article of any one of Embodiments 1 and 3, whereineach of the shaped abrasive particles or elongated abrasive particleshave a predetermined rotational orientation angle relative to a sidesurface of the body.

Embodiment 64

The fixed abrasive article of any one of Embodiments 2 and 63, whereinthe predetermined rotational orientation angle defines an angle betweena radial axis and a particle axis, wherein the predetermined rotationalorientation angle is less than 90 degrees.

Embodiment 65

The fixed abrasive article of any one of Embodiments 2 and 63, whereinthe average predetermined rotational orientation angle for the shapedabrasive particles or elongated abrasive particles is not greater than90 degrees or not greater than 80 degrees or not greater than 70 degreesor not greater than 60 degrees or not greater than 50 degrees or notgreater than 40 degrees or not greater than 30 degrees or not greaterthan 20 degrees or not greater than 10 degrees or not greater than 5degrees.

Embodiment 66

The fixed abrasive article of any one of Embodiments 2 and 63, whereinthe average predetermined rotational orientation angle for the shapedabrasive particles or elongated abrasive particles is at least 0.1degrees or at least 1 degree or at least 3 degrees or at least 5 degreesor at least 10 degrees or at least 20 degrees or at least 30 degrees orat least 40 degree or at least 50 degrees.

Embodiment 67

The fixed abrasive article of any one of Embodiments 2 and 63, wherein aportion of the shaped abrasive particles or elongated abrasive particlescomprises a standard deviation of predetermined rotational orientationangle of not greater than 20 degrees or not greater than 10 degrees ornot greater than 9 degrees or not greater than 8 degrees or not greaterthan 7 degrees or not greater than 6 degrees.

Embodiment 68

The fixed abrasive article of Embodiment 67, wherein the portionincludes at least one of a first group, a radial set, an axialcollection, and a combination thereof.

Embodiment 69

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the shaped abrasive particles or elongated abrasive particleshave a longitudinal axis extending substantially parallel to a majorsurface of the body.

Embodiment 70

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the shaped abrasive particles or elongated abrasive particleshave a longitudinal axis extending substantially perpendicular to theside surface of the body.

Embodiment 71

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the shaped abrasive particles or elongated abrasive particleshave a predetermined lateral axis rotational orientation angle.

Embodiment 72

The fixed abrasive article of Embodiment 71, wherein the averagepredetermined lateral axis rotational orientation angle of the shapedabrasive particles or elongated abrasive particles is not greater than90 degrees or not greater than 80 degrees or not greater than 70 degreesor not greater than 60 degrees or not greater than 50 degrees or notgreater than 40 degrees or not greater than 30 degrees or not greaterthan 20 degrees or not greater than 10 degrees or not greater than 5degrees.

Embodiment 73

The fixed abrasive article of Embodiment 71, wherein the averagepredetermined lateral axis rotational orientation angle for the shapedabrasive particles or elongated abrasive particles is at least 0.1degrees or at least 1 degree or at least 3 degrees or at least 5 degreeor at least 10 degrees or at least 20 degrees or at least 30 degrees orat least 40 degree or at least 50 degrees.

Embodiment 74

The fixed abrasive article of Embodiment 71, wherein a portion of theshaped abrasive particles or elongated abrasive particles comprises astandard deviation of the predetermined lateral axis rotationalorientation angle of not greater than 20 degrees or not greater than 10degrees or not greater than 9 degrees or not greater than 8 degrees ornot greater than 7 degrees or not greater than 6 degrees.

Embodiment 75

The fixed abrasive article of Embodiment 74, wherein the portionincludes at least one of a first group, a radial set, an axialcollection, and a combination thereof.

Embodiment 76

The fixed abrasive article of any one of Embodiments 1 and 2, wherein atleast a portion of the abrasive particles are coupled to an orientationstructure extending throughout a portion of the bond material within thebody.

Embodiment 77

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure has a different composition compared to thebond material.

Embodiment 78

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure defines a structure coupling at least aportion of the abrasive particles to one another and defining a separatephase from the bond material.

Embodiment 79

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure is coupled to a majority of the shapedabrasive particles or elongated abrasive particles.

Embodiment 80

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a material selected from the groupconsisting of a metal, a ceramic, a glass, an organic material, apolymer, and a combination thereof.

Embodiment 81

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure extends throughout an entire volume of thebody.

Embodiment 82

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure extends through at least a portion of theentire volume of the body.

Embodiment 83

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure is coupled to the abrasive particles andconfigured to control the predetermined rotational orientation of theabrasive particles within the body.

Embodiment 84

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a hardness less than a hardness ofthe bond material.

Embodiment 85

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a hardness less than a hardness ofthe abrasive particles.

Embodiment 86

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a web, a woven material, a non-wovenmaterial, paper, fabric, a spunwoven material, a film, a laminate, acomposite, a preform with regions sized to contain a shaped abrasiveparticle or elongated abrasive particle, and a combination thereof.

Embodiment 87

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure is coupled to the abrasive particles andconfigured to control a predetermined position including a radialposition, an axial position, and an angular position of the abrasiveparticles within the body.

Embodiment 88

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure is coupled to each of the shaped abrasiveparticles or elongated abrasive particles throughout the body.

Embodiment 89

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a hardness greater than a hardnessof the bond material.

Embodiment 90

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a hardness substantially the same asa hardness of the bond material.

Embodiment 91

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe orientation structure comprises a hardness substantially the same asa hardness of the abrasive particles.

Embodiment 92

The fixed abrasive article of any one of Embodiments 3 and 76, whereinthe body comprises a first orientation structure associated with a firstgroup of abrasive particles and a second orientation structure differentthan the first orientation structure associated with a second group ofabrasive particles.

Embodiment 93

The fixed abrasive article of Embodiment 92, wherein the firstorientation structure is associated with a first group of abrasiveparticles within a first radial plane and the second orientationstructure is associated with a second group of abrasive particles withina second radial plane.

Embodiment 94

The fixed abrasive article of Embodiment 92, wherein the firstorientation structure is associated with a first radial set of abrasiveparticles within a first radial plane and the second orientationstructure is associated with a second radial set of abrasive particles.

Embodiment 95

The fixed abrasive article of Embodiment 92, wherein the firstorientation structure is associated with a first axial collection ofabrasive particles within a first axial plane and the second orientationstructure is associated with a second axial collection of abrasiveparticles within a second axial plane.

Embodiment 96

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the abrasive particles comprise a material selected from thegroup consisting of oxides, carbides, nitrides, borides, oxycarbides,oxynitrides, oxyborides, diamond, carbon-containing materials, and acombination thereof, or wherein the abrasive particles comprise amonocrystalline material, polycrystalline material, a vitreous material,and a combination thereof, or wherein the abrasive particles comprise atleast one material selected from the group consisting of alumina,zirconia, magnesia, rare-earth oxides, and a combination thereof.

Embodiment 97

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the abrasive particles further comprise particles selected fromthe group consisting of diluent particles, agglomerated particles,natural particles, synthetic particles, and a combination thereof.

Embodiment 98

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the shaped abrasive particles comprise a material selected fromthe group consisting of oxides, carbides, nitrides, borides,oxycarbides, oxynitrides, oxyborides, diamond, carbon-containingmaterials, and a combination thereof, or wherein the shaped abrasiveparticles comprise a monocrystalline material, polycrystalline material,a vitreous material, and a combination thereof, or wherein the shapedabrasive particles comprise at least one material selected from thegroup consisting of alumina, zirconia, magnesia, rare-earth oxides, anda combination thereof.

Embodiment 99

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body including at least about 95 wt % aluminafor the total weight of the body.

Embodiment 100

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body including not greater than about 99.5 wt% alumina for the total weight of the body.

Embodiment 101

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a polycrystalline materialincluding crystalline grains, wherein the average grain size is notgreater than about 1 micron.

Embodiment 102

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a polycrystalline materialincluding crystalline grains, wherein the average grain size is at leastabout 0.01 microns.

Embodiment 103

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body that is essentially free of a binder, orwherein the body is essentially free of an organic material, or whereinthe body is essentially free of rare earth elements, or wherein the bodyis essentially free of iron, or wherein the body is formed from a seededsol gel.

Embodiment 104

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a two-dimensional shape asviewed in a plane defined by a length and a width of the body selectedfrom the group consisting of polygons, ellipsoids, numerals, Greekalphabet characters, Latin alphabet characters, Russian alphabetcharacters, complex shapes having a combination of polygonal shapes, anda combination thereof.

Embodiment 105

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a triangular two-dimensionalshape.

Embodiment 106

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a three-pointed startwo-dimensional shape.

Embodiment 107

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body, and the body comprises at least one tiphaving a tip sharpness of not greater than 80 microns or not greaterthan 70 microns or not greater than 60 microns or not greater than 50microns.

Embodiment 108

The fixed abrasive article of Embodiment 107, wherein the tip comprisesa tip sharpness of at least 1 micron.

Embodiment 109

The fixed abrasive article of Embodiment 98, wherein each of the shapedabrasive particles have a body comprising a length (l), a width (w), anda height (hi), wherein the length≥width, the length≥height, and thewidth≥height.

Embodiment 110

The fixed abrasive article of Embodiment 109, wherein the height (h) isat least about 100 microns the width not greater than about 5 mm and thelength not greater than 5 mm.

Embodiment 111

The fixed abrasive article of Embodiment 109, wherein the body comprisesa primary aspect ratio of length:width of at least about 1:1 and notgreater than about 10:1.

Embodiment 112

The fixed abrasive article of Embodiment 109, wherein the body comprisesa secondary aspect ratio defined by a ratio of width:height within arange between about 5:1 and about 1:1.

Embodiment 113

The fixed abrasive article of Embodiment 109, wherein the body comprisesa tertiary aspect ratio defined by a ratio of length:height within arange between about 6:1 and about 1:1.

Embodiment 114

The fixed abrasive article of Embodiment 109, wherein the body comprisesa dishing value (d) of not greater than about 2 or not greater thanabout 1.5 or not greater than about 1.2.

Embodiment 115

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body further comprises an additive selected from the groupconsisting of fillers, grinding aids, pore inducers, hollow materials,catalysts, coupling agents, curants, anti-static agents, suspendingagents, anti-loading agents, lubricants, wetting agents, dyes, fillers,viscosity modifiers, dispersants, defoamers, and a combination thereof.

Embodiment 116

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a side surface configured to conduct amaterial removal operation.

Embodiment 117

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a porosity within a range including 0.5 vol %and 80 vol % for a total volume of the body.

Embodiment 118

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a content of abrasive particles within arange including at least 0.5 vol % and not greater than 50 vol % for atotal volume of the body.

Embodiment 119

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a content of bond material within a rangeincluding at least 0.5 vol % and not greater than 50 vol % for a totalvolume of the body.

Embodiment 120

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body is in the form of a thin wheel having a ratio ofdiameter:thickness of at least 10:1 or at least 50:1 or at least 100:1.

Embodiment 121

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a thickness of not greater than 10 mm.

Embodiment 122

The fixed abrasive article of any one of Embodiments 1, 2, and 3,wherein the body comprises a diameter of at least 20 mm.

Embodiment 123

A method of forming a fixed abrasive article comprising:

forming a mixture including a precursor bond material;

providing a forming structure configured to position abrasive particlescomprising shaped abrasive particles or elongated abrasive particleseach having an aspect ratio of length:width of at least 1.1:1, in apredetermined position within the precursor bond material; and

treating the green body to form a fixed abrasive article having a bodyand wherein each of the abrasive particles have a predetermined positionwithin the body and a predetermined rotational orientation relative to aside surface of the body.

Embodiment 124

The method of Embodiment 123, wherein the precursor bond materialcomprises a material selected from the group consisting of a ceramic, aglass, a frit, an organic material, a polymer, a metal, and acombination thereof.

Embodiment 125

The method of Embodiment 123, wherein the precursor bond materialincludes a powder.

Embodiment 126

The method of Embodiment 123, wherein the forming structure comprises atleast one opening and the abrasive particles are configured to passthrough the at least one opening for deposition in the precursor bondmaterial in a predetermined position.

Embodiment 127

The method of Embodiment 123, wherein the abrasive particles areconfigured to pass through the at least one opening for deposition in apredetermined position within the body of the fixed abrasive article.

Embodiment 128

The method of Embodiment 127, wherein the abrasive particles areconfigured to pass through the at least one opening for deposition inthe precursor bond material in a predetermined rotational orientationrelative to a side surface of the body of the fixed abrasive article.

Embodiment 129

The method of Embodiment 127, wherein the forming structure isconfigured to move and control the predetermined position of a singleabrasive particle by controlling the position of the forming structurerelative to the precursor bond material.

Embodiment 130

The method of Embodiment 127, wherein the forming structure isconfigured to place a single abrasive particle at a time onto theprecursor bond material to control the predetermined position of each ofthe abrasive particles.

Embodiment 131

The method of Embodiment 123, wherein the forming structure comprises aplurality of openings.

Embodiment 132

The method of Embodiment 131, further comprising passing the abrasiveparticles through the openings in the forming structure for depositionof the abrasive particles into the precursor bond material with apredetermined position and predetermined rotational orientation relativeto a side surface.

Embodiment 133

The method of Embodiment 132, wherein passing the abrasive particlesthrough the openings in the forming structure includes passing anabrasive particle through an opening in the forming structure to placethe abrasive particle in the bond material with a predetermined positionand predetermined rotational orientation.

Embodiment 134

The method of Embodiment 132, wherein the openings are positioned on theforming structure to control the position of each of the abrasiveparticles within the precursor bond material.

Embodiment 135

The method of Embodiment 132, wherein the openings have a shapeconfigured to control the rotational orientation of the abrasiveparticles as the abrasive particles pass through the openings.

Embodiment 136

The method of Embodiment 132, wherein the openings have atwo-dimensional shape selected from the group consisting of a polygon,an ellipsoid, a numeral, a Greek alphabet character, a Latin alphabetcharacter, a Russian alphabet character, a complex shape having acombination of polygonal shapes, and a combination thereof.

Embodiment 137

The method of Embodiment 132, wherein the openings have substantiallythe same two-dimensional shape as the two-dimensional shape of theshaped abrasive particles or elongated abrasive particles.

Embodiment 138

The method of Embodiment 132, wherein the openings are arranged in adistribution within the forming structure.

Embodiment 139

The method of Embodiment 138, wherein the distribution of the openingscorresponds to the distribution of at least a portion of the abrasiveparticles within the body.

Embodiment 140

The method of Embodiment 123, wherein the process includes placing afirst group of abrasive particles in a first radial plane within theprecursor bond material.

Embodiment 141

The method of Embodiment 140, wherein the process includes placing afirst group of shaped abrasive particles or elongated particles in afirst radial plane within the precursor bond material.

Embodiment 142

The method of Embodiment 140, wherein the first group of abrasiveparticles is a layer of abrasive particles overlying a layer ofprecursor bond material.

Embodiment 143

The method of Embodiment 140, further comprising depositing precursorbond material over the first group of abrasive particles in the firstradial plane.

Embodiment 144

The method of Embodiment 143, further comprising depositing a secondgroup of abrasive particles in a second radial plane overlying the firstgroup of abrasive particle in the first radial plane.

Embodiment 145

The method of Embodiment 144, wherein the second group of abrasiveparticles is a layer overlying a layer of precursor bond material.

Embodiment 146

The method of Embodiment 144, wherein depositing the second group ofabrasive particle includes depositing the second group of abrasiveparticles on a layer of the precursor bond material disposed between thefirst group of abrasive particles and the second group of abrasiveparticles.

Embodiment 147

The method of Embodiment 144, further comprising treating the precursorbond material to form a bond material

Embodiment 148

The method of Embodiment 123, wherein the forming structure is temporarystructure that is not included within the fixed abrasive article.

Embodiment 149

The method of Embodiment 123, wherein the forming structure is anintegrated structure contained within the fixed abrasive article.

Embodiment 150

The method of Embodiment 123, wherein the abrasive particles arepermanently attached to the forming structure.

Embodiment 151

The method of Embodiment 123, wherein the abrasive particles aretemporarily in contact with the forming structure.

Embodiment 152

The method of Embodiment 123, wherein the forming structure is atemplate configured to control the predetermined position of theabrasive particles.

Embodiment 153

The method of Embodiment 123, wherein the forming structure is atemplate configured to control the predetermined rotational orientationof the abrasive particles relative to a side surface of the body of thefixed abrasive article.

Embodiment 154

The method of Embodiment 123, wherein the forming structure is a networkstructure including the abrasive particles coupled to each other bybridges.

Embodiment 155

The method of Embodiment 154, wherein the bridges are permanent and apart of the fixed abrasive article.

Embodiment 156

The method of Embodiment 154, wherein the bridges are temporary and thefixed abrasive article is essentially free of the bridges.

Embodiment 157

The method of Embodiment 154, wherein the bridges are consumed orremoved during processing to form the fixed abrasive article.

Embodiment 158

The method of Embodiment 154, wherein the bridges are removed duringtreating of the green body.

Embodiment 159

The method of Embodiment 123, wherein the mixture comprises theprecursor bond material and abrasive particles including shaped abrasiveparticles or elongated abrasive particles, wherein the mixture istranslated through the forming structure to form a layer of precursorbond material and abrasive particles having a predetermined rotationalorientation relative to a major surface of the layer.

Embodiment 160

The method of Embodiment 159, wherein the mixture is a wet mixture andthe mixture is poured through openings in the forming structure to forma layer of precursor bond material and abrasive particles having apredetermined rotational orientation relative to a major surface of thelayer.

Embodiment 161

The method of Embodiment 123, wherein the forming structure is selectedfrom a group of materials consisting of a metal, organic, resin,polymer, glass, ceramic, monocrystalline, polycrystalline, naturalmaterial, synthetic material, and a combination thereof.

Embodiment 162

The method of Embodiment 123, wherein the forming structure isconfigured to control a predetermined rotational orientation angle ofthe abrasive particles.

Embodiment 163

The method of Embodiment 162, wherein the predetermined rotationalorientation angle of the abrasive particles is not greater than 90degrees and at least 0.1 degrees.

Embodiment 164

The method of Embodiment 123, wherein the forming structure isconfigured to control a standard deviation of a predetermined rotationalorientation of a first group of abrasive particles.

Embodiment 165

The method of Embodiment 164, wherein the standard deviation of thepredetermined rotational orientation angle is not greater than 20degrees or not greater than 10 degrees or not greater than 9 degrees ornot greater than 8 degrees or not greater than 7 degrees or not greaterthan 6 degrees.

Embodiment 166

The method of any one of Embodiments 123-165, wherein providing theforming structure configured to position abrasive particles furthercomprises: depositing the abrasive particles and the precursor bondmaterial to form a preformed body.

Embodiment 167

The method of Embodiment 166, wherein depositing the abrasive particlesand the precursor bond material comprises extrusion.

Embodiment 168

The method of any one of Embodiments 123-167, wherein providing theforming structure configured to position abrasive particles furthercomprises: forming a mixture comprising the abrasive particles and theprecursor bond material; and extruding the mixture through the formingstructure to form a preformed body including the abrasive particles andthe precursor bond material.

Embodiment 169

The method of any one of Embodiments 167 and 168, wherein the preformedbody comprises a plurality of preformed bodies, wherein the plurality ofpreformed bodies are combined to form the fixed abrasive article.

Embodiment 170

The method of any one of Embodiments 123-169, wherein providing theforming structure configured to position abrasive particles is performedso as to form a plurality of elongated preformed structures.

Embodiment 171

The method of any one of Embodiments 23-170, wherein providing theforming structure configured to position abrasive particles is performedso as to form a plurality of preformed bodies.

Embodiment 172

The method of Embodiment 171, wherein the preformed bodies have a lengthand a maximum width, as measured in a direction perpendicular to thelength, and wherein the length is greater than the maximum width,wherein the length is at least 150% the maximum width, at least 175% themaximum width, at least 200% the maximum width, at least 250% themaximum width.

Embodiment 173

The method of any one of Embodiments 171 and 172, wherein the preformedbodies have an aspect ratio as measured by a ratio of length to amaximum width, as measured in a direction perpendicular to the length,and wherein the aspect ratio is at least 1.5, at least 2, at least 3, atleast 4, at least 5, at least 6, at least 7, at least 8, at least 9, atleast 10.

Embodiment 174

The method of any one of Embodiments 171-173, wherein the preformedbodies have an aspect ratio as measured by a ratio of length to amaximum width, as measured in a direction perpendicular to the length,and wherein the aspect ratio is less than 100, less than 50, less than25.

Embodiment 175

The method of any one of Embodiments 171-174, wherein the preformedbodies are generally cylindrical, wherein the pellets are cylindrical.

Embodiment 176

The method of any one of Embodiments 171-175, wherein the preformedbodies have first and second faces oriented parallel with respect toeach other and a cylindrical sidewall disposed between the first andsecond faces.

Embodiment 177

The method of any one of Embodiments 171-176, wherein the preformedbodies have an abrasive particle density, and wherein the abrasiveparticle density is higher than a mixture formed using a non-extrudedmethod.

Embodiment 178

The method of any one of Embodiments 171-177, wherein at least twoabrasive particles disposed in at least one preformed body have a samepredetermined three-axis orientation with respect to one another,wherein at least two abrasive particles disposed in each of thepreformed bodies have a same predetermined three-axis orientation withrespect to one another, wherein all abrasive particles disposed in atleast one of the preformed bodies have a same predetermined three-axisorientation with respect to one another, wherein all abrasive particlesdisposed in each of the preformed bodies have a same predeterminedthree-axis orientation with respect to one another.

Embodiment 179

A method of forming a fixed abrasive article comprising:

forming a mixture including a precursor bond material;

depositing abrasive particles comprising shaped abrasive particles orelongated abrasive particles each having an aspect ratio of length:widthof at least 1.1:1, into the precursor bond material to form a greenbody; and treating the green body to form a fixed abrasive articlehaving a body and abrasive particles contained in the body in apredetermined position and a predetermined rotational orientationrelative to a side surface of the body.

Embodiment 180

The method of Embodiment 179, wherein depositing includes forming theabrasive particles.

Embodiment 181

The method of Embodiment 180, wherein forming of the abrasive particlesis conducted during the process of forming the fixed abrasive article.

Embodiment 182

The method of Embodiment 180, wherein forming comprises: forming a firstportion of abrasive particles; depositing a first portion of a precursorbond material on the first portion of abrasive particles; and forming asecond portion of abrasive particles distinct from the first portion ofabrasive particles on the first portion of the precursor bond material.

Embodiment 183

The method of Embodiment 182, wherein the first portion includes atleast one of a first group, a first radial set, a first axialcollection, and a combination thereof.

Embodiment 184

The method of Embodiment 182, wherein the second portion includes atleast one of a second group, a second radial set, a second axialcollection, and a combination thereof.

Embodiment 185

The method of Embodiment 182, wherein forming the first portion includesforming a first portion of shaped abrasive particles or elongatedabrasive particles having a predetermined position or a predeterminedrotational orientation relative to a major surface of the body.

Embodiment 186

The method of Embodiment 182, wherein forming the first portion includesforming a first portion of shaped abrasive particles or elongatedabrasive particles having a predetermined position and a predeterminedrotational orientation relative to a major surface of the body.

Embodiment 187

The method of Embodiment 180, wherein forming comprises a processselected from the group consisting of additive manufacturing, printing,shaping, casting, stamping, molding, and a combination thereof.

Embodiment 188

The method of Embodiment 180, wherein forming comprises screen printingof the abrasive particles.

Embodiment 189

The method of Embodiment 180, wherein forming comprises screen printingof the shaped abrasive particles or elongated abrasive particles.

Embodiment 190

The method of Embodiment 180, wherein forming comprises 3D printing ofthe abrasive particles.

Embodiment 191

The method of Embodiment 180, wherein forming comprises 3D printing ofthe shaped abrasive particles or elongated abrasive particles.

Embodiment 192

The method of Embodiment 179, wherein depositing includes forming aforming structure including abrasive particles.

Embodiment 193

The method of Embodiment 192, wherein the forming structure comprisesabrasive particles coupled to each other by bridges.

Embodiment 194

The method of Embodiment 192, wherein the forming structure is formed by3D printing.

Embodiment 195

The method of Embodiment 192, wherein the forming structure isconfigured to control the predetermined position of the abrasiveparticles.

Embodiment 196

The method of Embodiment 192, wherein the forming structure isconfigured control a predetermined rotational orientation of theabrasive particles relative to a side surface of the body.

Embodiment 197

The method of Embodiment 179, further comprising treating the green bodyto form a fixed abrasive article having a body and abrasive particlescontained in the body in a predetermined position and a predeterminedrotational orientation relative to a side surface of the body.

Embodiment 198

The method of Embodiment 179, further comprising rearranging at least afirst portion of the abrasive particles to have a predeterminedrotational orientation.

Embodiment 199

The method of Embodiment 198, wherein rearranging includes changing thepredetermined rotational orientation of the abrasive particles.

Embodiment 200

The method of Embodiment 198, wherein rearranging includes changing thepredetermined rotational orientation of the abrasive particles withinthe precursor bond material.

Embodiment 201

The method of Embodiment 198, wherein rearranging includes changing thepredetermined rotational orientation of the abrasive particles to have astandard deviation of a predetermined rotational orientation angle ofnot greater than 20 degrees or not greater than 10 degrees or notgreater than 9 degrees or not greater than 8 degrees or not greater than7 degrees or not greater than 6 degrees.

Embodiment 202

The method of Embodiment 198, wherein rearranging includes providingenergy to the abrasive particles configured to cause a change in therotational orientation of the abrasive particles.

Embodiment 203

The method of Embodiment 202, wherein the energy is selected from thegroup consisting of electrical, mechanical, vibratory, electromagnetic,magnetic, sonic, and a combination thereof.

Embodiment 204

The method of Embodiment 198, wherein rearranging includes providing aforce to the abrasive particles configured to cause a change in therotational orientation of the abrasive particles.

Embodiment 205

The method of Embodiment 204, wherein the force is selected from thegroup consisting of gravity, centrifical, centrifugal, uniaxial,biaxial, isometric, and a combination thereof.

Embodiment 206

A method of forming a fixed abrasive article comprising:

forming a mixture including a precursor bond material;

providing a forming structure configured to position abrasive particlescomprising shaped abrasive particles or elongated abrasive particleseach having an aspect ratio of length:width of at least 1.1:1, in apredetermined position within the precursor bond material;

passing the precursor bond material and abrasive particles through theforming structure to form a plurality of preformed bodies, eachpreformed body comprising an elongated particle; treating the pluralityof preformed bodies to form a fixed abrasive article having a body,wherein each of the abrasive particles have a predetermined positionwithin the body or a predetermined three-axis orientation.

Embodiment 207

The method of Embodiment 206, wherein the precursor bond materialcomprises a material selected from the group consisting of a ceramic, aglass, a frit, an organic material, a polymer, a metal, and acombination thereof.

Embodiment 208

The method of Embodiment 206, wherein the precursor bond materialincludes a powder.

Embodiment 209

The method of Embodiment 206, further comprising treating the preformedbodies to form a fixed abrasive article having a body, wherein at leasta majority of the abrasive particles have a predetermined positionwithin the body and a predetermined three-axis orientation.

Embodiment 210

The method of Embodiment 206, wherein the forming structure comprises atleast one opening and the abrasive particles are configured to passthrough the at least one opening for deposition in the precursor bondmaterial in a predetermined position or a predetermined three-axisorientation.

Embodiment 211

The method of Embodiment 206, wherein passing the abrasive particlesthrough the openings in the forming structure comprises extruding theprecursor bond material and abrasive particles.

Embodiment 212

The method of Embodiment 211, wherein the forming structure is adaptedto control the position of each of the abrasive particles within theprecursor bond material.

Embodiment 213

The method of Embodiment 211, wherein the forming structure has anopening with a shape configured to control the rotational orientation ofthe abrasive particles as the abrasive particles pass through theforming structure.

Embodiment 214

The method of Embodiment 211, wherein the forming structure has anopening with a two-dimensional shape selected from the group consistingof a polygon, an ellipsoid, a numeral, a Greek alphabet character, aLatin alphabet character, a Russian alphabet character, a complex shapehaving a combination of polygonal shapes, and a combination thereof.

Embodiment 215

The method of Embodiment 211, wherein the forming structure has anopening with substantially the same two-dimensional shape as thetwo-dimensional shape of the shaped abrasive particles or elongatedabrasive particles.

Embodiment 216

The method of Embodiment 211, wherein the forming structure comprises aplurality of openings.

Embodiment 217

The method of Embodiment 206, wherein the abrasive particles arehomogeneously distributed throughout each of the preformed bodies.

Embodiment 218

The method of Embodiment 206, wherein the forming structure is atemporary structure that is not included within the fixed abrasivearticle.

Embodiment 219

The method of Embodiment 206, wherein the forming structure is anintegrated structure contained within the fixed abrasive article.

Embodiment 220

The method of Embodiment 206, wherein the abrasive particles arepermanently attached to the forming structure.

Embodiment 221

The method of Embodiment 206, wherein the abrasive particles aretemporarily in contact with the forming structure.

Embodiment 222

The method of Embodiment 206, wherein the forming structure is atemplate configured to control the predetermined position of theabrasive particles.

Embodiment 223

The method of Embodiment 206, wherein the forming structure is a networkstructure including the abrasive particles coupled to each other bybridges.

Embodiment 224

The method of Embodiment 206, wherein the mixture comprises theprecursor bond material and abrasive particles including shaped abrasiveparticles or elongated abrasive particles, wherein the mixture istranslated through the forming structure to form a plurality ofelongated particles, and wherein the abrasive particles have apredetermined rotational orientation relative to a major surface of theelongated particles.

Embodiment 225

The method of Embodiment 206, wherein the mixture is a wet mixture andthe mixture is poured through openings in the forming structure.

Embodiment 226

The method of Embodiment 206, wherein the forming structure is selectedfrom a group of materials consisting of a metal, organic, resin,polymer, glass, ceramic, monocrystalline, polycrystalline, naturalmaterial, synthetic material, and a combination thereof.

Embodiment 227

The method of Embodiment 206, wherein the forming structure isconfigured to control a predetermined tilt angle of the abrasiveparticles.

Embodiment 228

The method of Embodiment 227, wherein the tilt angle is 0 degrees.

Embodiment 229

The method of Embodiment 227, wherein the tilt angle is greater than 0degrees at least 2 degrees or at least 4 degrees or at least 6 degreesor at least 8 degree or at least 10 degrees or at least 15 degrees or atleast 20 degrees or at least 25 degrees or at least 30 degrees or atleast 35 degree or at least 45 degrees or at least 50 degrees or atleast 55 degrees or at least 60 degrees or at least 65 degrees or atleast 70 degree or at least 75 degrees or at least 80 degrees.

Embodiment 230

The method of Embodiment 227, wherein the tilt angle is not greater than90 degrees or not greater than 88 degrees or not greater than 85 degreesor not greater than 80 degrees or not greater than 75 degrees or notgreater than 70 degrees or not greater than 65 degrees or not greaterthan 60 degrees or not greater than 55 degrees or not greater than 50degrees or not greater than 45 degrees or not greater than 40 degrees ornot greater than 35 degrees or not greater than 30 degrees or notgreater than 25 degrees or not greater than 20 degrees or not greaterthan 15 degrees or not greater than 10 degrees or not greater than 8degrees or not greater than 6 degrees.

Embodiment 231

The method of Embodiment 227, further comprising a tilt angle variationof the abrasive particles of not greater than 10 degrees with respect toeach other or not greater than 8 degrees or not greater than 6 degreesor not greater than 5 degrees or not greater than 4 degrees or notgreater than 3 degrees or not greater than 2 degrees.

The above-disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended items are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true scope of the present invention. Thus, to the maximum extentallowed by law, the scope of the present invention is to be determinedby the broadest permissible interpretation of the following items andtheir equivalents, and shall not be restricted or limited by theforegoing detailed description.

The Abstract of the Disclosure is provided to comply with patent Law andis submitted with the understanding that it will not be used tointerpret or limit the scope or meaning of the claims. In addition, inthe foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all features of any of the disclosed embodiments. Thus, thefollowing claims are incorporated into the Detailed Description, witheach claim standing on its own as defining separately claimed subjectmatter.

What is claimed is:
 1. A fixed abrasive article comprising: a bodyhaving abrasive particles contained within a bond material, the abrasiveparticles including a plurality of shaped abrasive particles orelongated abrasive particles having an aspect ratio of length:width ofat least 1.1:1, each of the shaped abrasive particles or elongatedabrasive particles having a predetermined rotational orientation anglerelative to a side surface of the body, wherein the predeterminedrotational orientation is distinct from conventional abrasive articleshaving abrasive particles having a random orientation, is the anglebetween the longitudinal axis of the shaped abrasive particle orelongated abrasive particle and the radial axis in a plane defined by alength and a width of the shaped abrasive particle or elongated abrasiveparticle, and wherein at least 50% of the shaped abrasive particles orelongated abrasive particles of the total amount of abrasive particleshave a rotational orientation of 0 degrees to about 50 degrees.
 2. Thefixed abrasive article of claim 1, wherein each of the shaped abrasiveparticles or elongated abrasive particles have a predetermined positionand a predetermined three-axis orientation.
 3. The fixed abrasivearticle of claim 1, wherein each of the shaped abrasive particlescomprises a cutting tip or cutting edge having a predeterminedrotational orientation relative to the side surface.
 4. The fixedabrasive article of claim 1, wherein the body comprises a first group ofabrasive particles positioned within a first radial plane within thebody, each of the abrasive particles of the first group having apredetermined rotational orientation within the first radial planerelative to the side surface of the body, and wherein the body comprisesa second group of abrasive particles within a second radial plane withinthe body, each of the abrasive particles of the second group having apredetermined rotational orientation within the second radial planerelative to the side surface of the body.
 5. The fixed abrasive articleof claim 4, wherein the abrasive particles of the first group ofabrasive particles are arranged in a controlled distribution relative toeach other and wherein a second group of abrasive particles are arrangedin a controlled distribution relative to each other.
 6. The fixedabrasive article of claim 5, wherein the controlled distribution of atleast one of the first group of abrasive particles and the second groupof abrasive particles comprises a phyllotactic pattern.
 7. The fixedabrasive article of claim 5, wherein an abrasive particle of the firstgroup of abrasive particles is radially and axially staggered relativeto an abrasive particle of the second group of abrasive particles. 8.The fixed abrasive article of claim 4, wherein the abrasive particleswithin the first group have a predetermined position havingsubstantially the same axial position within the first radial plane withrespect to each other and wherein the abrasive particles within thesecond group have a predetermined position having substantially the sameaxial position within the second radial plane with respect to eachother.
 9. The fixed abrasive article of claim 8, wherein the abrasiveparticles of the first group comprise a different radial position withrespect to each other and wherein the abrasive particles of the secondgroup comprise a different radial position with respect to each other.10. The fixed abrasive article of claim 4, wherein the first radialplane and second radial plane are axially spaced apart from each otherwithin the body.
 11. The fixed abrasive article of claim 4, wherein thefirst group of abrasive particles have a first predetermined rotationalorientation and the second group of abrasive particles have a secondpredetermined rotational orientation different than the firstpredetermined rotational orientation.
 12. The fixed abrasive article ofclaim 4, wherein the abrasive particles of the first group and thesecond group have at least one abrasive characteristic that isdifferent.
 13. The fixed abrasive article of claim 1, wherein the bodycomprises a plurality of groups of abrasive particles associated with aplurality of different radial planes within the body, and wherein eachgroup of the plurality of groups of abrasive particles includes aplurality of radial sets of abrasive particles, wherein each of theradial sets are spaced at a different radial distance from a center ofthe body relative to each other.
 14. The fixed abrasive article of claim1, wherein the body comprises a first axial collection of abrasiveparticles within a first axial plane within the body, each of theabrasive particles of the first axial collection having a predeterminedrotational orientation relative to the side surface of the body, andwherein the body further comprises a second axial collection of abrasiveparticles within a second axial plane within the body that is differentthan the first axial plane, each of the abrasive particles of the secondaxial collection having a predetermined rotational orientation withinthe second axial plane relative to the side surface of the body.
 15. Thefixed abrasive article of claim 1, wherein the predetermined rotationalorientation angle defines an angle between a radial axis and a particleaxis, wherein the predetermined rotational orientation angle is betweenabout 0.1 degrees and about 90 degrees.
 16. The fixed abrasive articleof claim 1, wherein the shaped abrasive particles or elongated abrasiveparticles have a predetermined lateral axis rotational orientation anglebetween about 0.1 degrees and about 90 degrees.
 17. The fixed abrasivearticle of claim 1, wherein not greater than 50% of the shaped abrasiveparticles or elongated abrasive particles of the total amount ofabrasive particles have a rotational orientation of 60 degrees to about90 degrees.
 18. The fixed abrasive article of claim 1, wherein at least20% of the shaped abrasive particles or elongated abrasive particles ofthe total amount of abrasive particles have a rotational orientation of0 degrees to 20 degrees.
 19. The fixed abrasive article of claim 1,wherein at least 30% of the shaped abrasive particles or elongatedabrasive particles of the total amount of abrasive particles have arotational orientation of 0 degrees to 30 degrees.